{
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   "source": [
    " # <center>Lecture 2: Bayes' Rule  </center>  \n",
    " \n",
    " ## <center> Instructor: Dr. Hu Chuan-Peng  </center>"
   ]
  },
  {
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    "tags": []
   },
   "source": [
    "## Part 1: 【和鲸平台】整合教学+练习"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da2fadbd",
   "metadata": {
    "_id": "CBD7BE6CEACC42E3AF2D5C273FF36CB9",
    "id": "BEFCC0314A7D4512A71949B9014BB295",
    "jupyter": {},
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    "runtime": {
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     "is_visible": false,
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    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "本学期的贝叶斯课程将通过和鲸平台进行授课与代码练习，请大家提前注册好和鲸平台的账号。  \n",
    "\n",
    "关于和鲸平台的运行环境设置说明如下：  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjmwr1smy0.jpeg?imageView2/0/w/960/h/960)  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjmwr8pj5w.jpeg?imageView2/0/w/960/h/960)  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a62c87ef",
   "metadata": {
    "_id": "24FAE016A55E44179F8054656732F0B1",
    "id": "C35CF4E9CA30486B9A933D02510DD77A",
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    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "更重要的是：任何问题都可以微信群或者平台里发帖提问。  \n",
    "\n",
    "助教和老师会尽快回复的 🚀。  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjkvf5nlsl.jpeg?imageView2/0/w/960/h/960)  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjkvfd5d65.jpeg?imageView2/0/w/960/h/960)  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
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    "_id": "3B3A1C3022C74C848C83413419C2C33F",
    "id": "7AEA60D19ED649F1987F8443BFED18A2",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
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    },
    "scrolled": false,
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    },
    "tags": []
   },
   "source": [
    "当然，你也可以选择在gitee上进行提问。  \n",
    "点击链接访问gitee：  \n",
    "https://gitee.com/hcp4715/bayesian-analysis-nnupsy  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjkvfsm4c1.jpeg?imageView2/0/w/960/h/960)  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cee7fc55",
   "metadata": {
    "_id": "959962DB732A4DB59441904EFB17C296",
    "id": "9F87F45FBA584B159AD797C83EC0AFCA",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
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   },
   "source": [
    " ## Part 2: 单一事件的贝叶斯模型"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f16e850",
   "metadata": {
    "_id": "97A69A3273D64E7AA2D2CC8C6977E4B9",
    "id": "A5FB09585E8E4156A8760A4184E67F2E",
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   },
   "source": [
    "## **“让我们从一个每个人都熟悉的事件开始”**  \n",
    "\n",
    "读文献时，大家是否有一个疑问：我看到的这个文章靠谱吗？  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjpbvjqzx2.jpg?imageView2/0/w/640/h/640)  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdff1550",
   "metadata": {
    "_id": "2E3BD9AE42324A669E83F4E27A2D3047",
    "id": "08164BD956FB4ED9AEBDEC8683FC2684",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
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    },
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   },
   "source": [
    "2015年，**开放科学合作组织（Open Science Collaboration）** 在《Science》杂志上发表文章，发现只有**36%～47%** 的认知/社会心理学研究成果能被成功重复。  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjos6fmkbs.png?imageView2/0/w/960/h/960)  \n",
    "\n",
    "\n",
    "> Open Science Collaboration ,Estimating the reproducibility of psychological science.Science349,aac4716(2015).DOI:10.1126/science.aac4716"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea988b9c",
   "metadata": {
    "_id": "927FC0DD195D47A09AFCAFEECAA90F9E",
    "id": "93BFD96EA4234697B38A9E76E81579CD",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
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   },
   "source": [
    "以这个论文为代表的系列讨论，引发了关于心理学“可重复性危机”的讨论[(胡传鹏等, 2018)](https://journal.psych.ac.cn/xlkxjz/CN/10.3724/SP.J.1042.2016.01504)。  \n",
    "\n",
    "知道这个事实之后，对我们阅读文章时对结果的信念是否产生了影响？  \n",
    "\n",
    "假设我们认同Science这个文章的结论，初步认为大约**40%** 的心理学实验是可重复的。我们以这个数据作为我们对文章的初步“信念”。  \n",
    "\n",
    "新的关于心理学研究可重复性的研究是否会进一步改变我们的信念？"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6779af1",
   "metadata": {
    "_id": "A17CA82F36AF4B1B9D9D426183B62303",
    "id": "FE68156606064582965D4F883A597801",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
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   },
   "source": [
    "2024年，一项针对299项预注册的重复实验数据的研究发现，可重复研究通常以自信、透明和确切的语言撰写，而不可重复的研究则往往表现出模糊性，并使用“边缘型”的说服技巧。  \n",
    "\n",
    "这个新研究可能帮助我们**更新**对心理学科学论文的预测。  \n",
    "\n",
    "假定我们现在从上述299个文章中抽取出一篇论文，我们会如何评估它的可重复性？  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjoly6dhft.png?imageView2/0/w/960/h/960)  \n",
    "\n",
    "\n",
    "> Herzenstein, M., Rosario, S., Oblander, S., & Netzer, O. (2024). The language of (non)replicable social science. Psychological Science, 9567976241254037. https://doi.org/10.1177/09567976241254037  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f090298a",
   "metadata": {
    "_id": "0431DA1DBB18442E8023EB69490F4AB1",
    "id": "6A211583330A425087AFE8E531EB516A",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
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    },
    "scrolled": false,
    "slideshow": {
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    },
    "tags": []
   },
   "source": [
    "基于我们第一个研究（即认为大约40%的研究可以重复）和新证据（可重复性研究通常使用确切语言撰写），我们对随机抽取出的一项研究的可重复性的态度怎样呢？  \n",
    "\n",
    "假如我们仅根据*Science*的研究结果，我们可能会认为这项研究大约有40%可能性被重复出来？但是这意味着2024年新研究的信息没有被用上。  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "898eef56",
   "metadata": {
    "_id": "8276AE623A8941DD95D88D69E9C128F5",
    "id": "671F102509D84E7ABAE180900E513E50",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
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    },
    "scrolled": false,
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    },
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   },
   "source": [
    "根据Herzenstein 等（2024）的研究结果，可重复的研究中，有56%的文章使用确切的语言风格；在不可重复的研究中，使用确切语言的比例为为45%。  \n",
    "\n",
    "根据这些信息，我们可以得到以下几个关键信息：  \n",
    "- 心理学研究可重复的概率为40%  \n",
    "- 心理学研究不可重复的概率为60%  \n",
    "- 可重复的研究中，使用确切语言的概率为56%  \n",
    "- 不可重复的研究中，使用确切语言的概率为45%  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjoxpj2ivv.png?imageView2/0/w/640/h/640)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d76fa7de",
   "metadata": {
    "_id": "21789174E0044E24B1CA5DDC803C1D4F",
    "id": "16743F0B8EA64A5BA5A6FBE093EAD1D1",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
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     "is_visible": false,
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    },
    "scrolled": false,
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    },
    "tags": []
   },
   "source": [
    "根据上述信息，现在我们可以进行以下的简单的运算：  \n",
    "\n",
    "- 研究可重复且使用确切语言的概率 $P = 0.40 \\times 0.56 = 0.224$  \n",
    "- 研究可重复但不使用确切语言的概率 $P= 0.40 * (1-0.56) = 0.176$  \n",
    "- 研究不可重复但使用确切语言的概率 $P= 0.60 * 0.45 = 0.27$  \n",
    "- 研究不可重复且不使用确切语言的概率 $P= 0.60 * (1-0.45) = 0.33$  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjp0bqwjgl.png?imageView2/0/w/960/h/960)  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "057bba6a",
   "metadata": {
    "_id": "9A966B81FDF3433B90DB37EEA7449D65",
    "id": "3CAA210B428B4726AF564BF99B932FAC",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "假如我们抽取出一个文章使用了确切的语言风格，我们认为它可重复的可能性是多少呢？  \n",
    "\n",
    "$0.224/(0.224 + 0.27) = 0.453$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "984e10a7",
   "metadata": {
    "_id": "7B86ECDD3D8C4CF4BC570379B7B8D4E0",
    "id": "F30C9DF8692247DD80290DEE244DF8D5",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "在这个简单的例子当中，我们实际进行了一次“贝叶斯的证据更新”。  \n",
    "\n",
    "接下来我们再来重新审视一下这个事例。  \n",
    "\n",
    "我们选取Herzenstein 等（2024）年的部分真实数据进行探索，包括研究的编号 (title)，文章是否可被重复 (replicated), 文章结果描述的确切性 (certain)和文章表述的积极性 (posemo)。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "86c40a4c",
   "metadata": {
    "_id": "6650178E299B46A59FCD49B10A2F19CA",
    "collapsed": false,
    "id": "C4211626E59A44BCB2085B9505C99F01",
    "jupyter": {
     "outputs_hidden": false
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    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
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    "tags": []
   },
   "outputs": [],
   "source": [
    "# 非选课的同学，可以使用和鲸社区的Python镜像，运行以下的代码安装必要的模块，需要3-5分钟的时间完成加载\n",
    "# 后续会有专门的社区公开镜像，给大家提前配置好运行环境\n",
    "# 将下列代码行解除注释，删除“#”，运行即可：\n",
    "# !conda install -y graphviz bambi=0.13.0 pymc=5.16.2 PreliZ=0.9.0 ipympl=0.9.4 pingouin=0.5.4\n",
    "\n",
    "# docker部署和使用教程链接：https://zhuanlan.zhihu.com/p/719739087\n",
    "# docker pull hcp4715/pybaysian:latest\n",
    "# docker run -it --rm -p 8888:8888 hcp4715/pybaysian:latest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4a7244bb",
   "metadata": {
    "_id": "5E2EC868AAD6488CA5E5DFADCF965A1A",
    "collapsed": false,
    "id": "76867943A901493595AFDC8873B9561A",
    "jupyter": {
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    "slideshow": {
     "slide_type": "slide"
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   "source": [
    "# 安装和加载包\n",
    "options(repos = c(CRAN = \"https://mirrors.tuna.tsinghua.edu.cn/CRAN/\"))\n",
    "if (!requireNamespace('pacman', quietly = TRUE)) {\n",
    "    install.packages('pacman')\n",
    "}\n",
    "pacman::p_load(\"tidyverse\",\"ggplot2\",\"dplyr\",\"car\",\"ggpubr\",'rstan',\n",
    "               \"BayesFactor\",\"bayestestR\",\"gridExtra\",\"TOSTER\")\n",
    "options(warn = -1)  # 抑制警告\n",
    "\n",
    "#设置APA画图格式\n",
    "APA_theme <- theme(\n",
    "  plot.margin = unit(c(1, 1, 1, 1), \"cm\"),\n",
    "  panel.background = element_blank(), \n",
    "  plot.title = element_text(size = 16, face = \"bold\",hjust = 0.5,margin = margin(b = 15)),\n",
    "  axis.line = element_line(color = \"black\"),\n",
    "  axis.title = element_text(size = 16, color = \"black\",face = \"bold\"),\n",
    "  axis.text = element_text(size = 16, color = \"black\"),\n",
    "  axis.text.x = element_text(margin = margin(t = 10)),\n",
    "  axis.text.y = element_text(size = 16),\n",
    "  axis.title.y = element_text(margin = margin(r = 10)),\n",
    "  axis.ticks.x = element_blank(),\n",
    "  legend.background = element_rect(color = \"black\"),\n",
    "  legend.text = element_text(size = 15),\n",
    "  legend.margin = margin(t = 5, l = 5, r = 5, b = 5),\n",
    "  legend.key = element_rect(color = NA, fill = NA)\n",
    "  )\n",
    "\n",
    "#导入数据\n",
    "df <- tryCatch({\n",
    "  read.csv('/home/mw/input/bayes3797/replicated_language_cleaned.csv') #平台路径\n",
    "}, error = function(e) {\n",
    "  read.csv('/Users/liumingyu/Desktop/1/PyBayesian/data/replicated_language_cleaned.csv') #本地路径\n",
    "})\n",
    "\n",
    "#整理数据（删除特定列）\n",
    "df <- df %>% select(-study_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "501565d7",
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    "_id": "7220F66CE63E4264AD38AC5B6A7C50A3",
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    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>study_id</th><th scope=col>replicated</th><th scope=col>posemo</th><th scope=col>certain</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1</td><td>1</td><td>1.36</td><td>1.75</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>3</td><td>0</td><td>1.92</td><td>1.17</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>4</td><td>1</td><td>1.41</td><td>1.36</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>5</td><td>0</td><td>1.85</td><td>0.69</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>6</td><td>0</td><td>0.63</td><td>0.72</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>7</td><td>0</td><td>1.26</td><td>0.77</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & study\\_id & replicated & posemo & certain\\\\\n",
       "  & <chr> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 1 & 1 & 1.36 & 1.75\\\\\n",
       "\t2 & 3 & 0 & 1.92 & 1.17\\\\\n",
       "\t3 & 4 & 1 & 1.41 & 1.36\\\\\n",
       "\t4 & 5 & 0 & 1.85 & 0.69\\\\\n",
       "\t5 & 6 & 0 & 0.63 & 0.72\\\\\n",
       "\t6 & 7 & 0 & 1.26 & 0.77\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 4\n",
       "\n",
       "| <!--/--> | study_id &lt;chr&gt; | replicated &lt;dbl&gt; | posemo &lt;dbl&gt; | certain &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 | 1 | 1 | 1.36 | 1.75 |\n",
       "| 2 | 3 | 0 | 1.92 | 1.17 |\n",
       "| 3 | 4 | 1 | 1.41 | 1.36 |\n",
       "| 4 | 5 | 0 | 1.85 | 0.69 |\n",
       "| 5 | 6 | 0 | 0.63 | 0.72 |\n",
       "| 6 | 7 | 0 | 1.26 | 0.77 |\n",
       "\n"
      ],
      "text/plain": [
       "  study_id replicated posemo certain\n",
       "1 1        1          1.36   1.75   \n",
       "2 3        0          1.92   1.17   \n",
       "3 4        1          1.41   1.36   \n",
       "4 5        0          1.85   0.69   \n",
       "5 6        0          0.63   0.72   \n",
       "6 7        0          1.26   0.77   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "head(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57529688",
   "metadata": {
    "_id": "D1AB055B5890484881A9BA656B67D054",
    "id": "E55F6A87BA9D426495965ED34E9059CF",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
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    },
    "scrolled": false,
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    },
    "tags": []
   },
   "source": [
    "### 先验 (prior) 和 数据 (data)  \n",
    "\n",
    "重新回顾我们要评估的事件：我们认为从299项心理学研究中随机选出来的一项研究的可重复性如何？  \n",
    "\n",
    "在评估这个事件之前，我们知道Science于2015年发表了一个大规模重复实验，发现40%的心理学研究是可以被重复出来。  \n",
    "\n",
    "对于这299项研究，它们有不同的语言风格："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "39e4d9d7",
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    "_id": "69527C9D804D4A6B931487113C2E71BF",
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    "id": "6CAFB9DF235941A9B9D2CFF5786417ED",
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   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>study_id</th><th scope=col>replicated</th><th scope=col>posemo</th><th scope=col>certain</th><th scope=col>language_style</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1</td><td>1</td><td>1.36</td><td>1.75</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>3</td><td>0</td><td>1.92</td><td>1.17</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>4</td><td>1</td><td>1.41</td><td>1.36</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>5</td><td>0</td><td>1.85</td><td>0.69</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>6</td><td>0</td><td>0.63</td><td>0.72</td><td>0</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>7</td><td>0</td><td>1.26</td><td>0.77</td><td>0</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       "  & study\\_id & replicated & posemo & certain & language\\_style\\\\\n",
       "  & <chr> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 1 & 1 & 1.36 & 1.75 & 1\\\\\n",
       "\t2 & 3 & 0 & 1.92 & 1.17 & 1\\\\\n",
       "\t3 & 4 & 1 & 1.41 & 1.36 & 1\\\\\n",
       "\t4 & 5 & 0 & 1.85 & 0.69 & 0\\\\\n",
       "\t5 & 6 & 0 & 0.63 & 0.72 & 0\\\\\n",
       "\t6 & 7 & 0 & 1.26 & 0.77 & 0\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 5\n",
       "\n",
       "| <!--/--> | study_id &lt;chr&gt; | replicated &lt;dbl&gt; | posemo &lt;dbl&gt; | certain &lt;dbl&gt; | language_style &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| 1 | 1 | 1 | 1.36 | 1.75 | 1 |\n",
       "| 2 | 3 | 0 | 1.92 | 1.17 | 1 |\n",
       "| 3 | 4 | 1 | 1.41 | 1.36 | 1 |\n",
       "| 4 | 5 | 0 | 1.85 | 0.69 | 0 |\n",
       "| 5 | 6 | 0 | 0.63 | 0.72 | 0 |\n",
       "| 6 | 7 | 0 | 1.26 | 0.77 | 0 |\n",
       "\n"
      ],
      "text/plain": [
       "  study_id replicated posemo certain language_style\n",
       "1 1        1          1.36   1.75    1             \n",
       "2 3        0          1.92   1.17    1             \n",
       "3 4        1          1.41   1.36    1             \n",
       "4 5        0          1.85   0.69    0             \n",
       "5 6        0          0.63   0.72    0             \n",
       "6 7        0          1.26   0.77    0             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 数据预处理\n",
    "# 计算 'certain' 列的中位数\n",
    "median_certain <- median(df$certain)\n",
    "\n",
    "# 创建新列，编码规则：大于中位数为 1，小于等于中位数为 2\n",
    "df <- df %>%\n",
    "  mutate(language_style = ifelse(certain > median_certain, 1, 0))\n",
    "    \n",
    "# 输出结果\n",
    "head(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b45dfba",
   "metadata": {
    "_id": "7D0BAB067DCB4951B131492739ACE9A6",
    "id": "4CDFF11C64264DDB8FD8F372F508681B",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
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    },
    "tags": []
   },
   "source": [
    "研究能否被重复出来，与他们的语言风格有关系：  \n",
    "\n",
    "有 56%（71/126）的能被重复的研究使用了确切的语言风格；  \n",
    "\n",
    "约45%（78/173）的不能被重复研究使用了确切的语言风格。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "96ecdd6c",
   "metadata": {
    "_id": "EE563704B3464650B00D8CDEB623D3E9",
    "collapsed": false,
    "id": "535BB55719C14AD2A3F5060CFBCED79F",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  数量 百分比\n",
      "0  173  57.86\n",
      "1  126  42.14\n"
     ]
    }
   ],
   "source": [
    "# 计算不同水平的数量和百分比\n",
    "level_counts <- table(df$replicated)  # 计算数量\n",
    "level_percentages <- round(prop.table(level_counts) * 100, 2)  # 计算百分比并保留两位小数\n",
    "# 创建一个新的数据框合并结果\n",
    "result_df1 <- as.data.frame(t(rbind(level_counts,level_percentages)))\n",
    "colnames(result_df1) <- c(\"数量\", \"百分比\")\n",
    "\n",
    "# 显示结果（0代表不可重复，1代表可重复）\n",
    "print(result_df1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9eae5fbd",
   "metadata": {
    "_id": "3216FB04D2094FABBE7FBDE352C58000",
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    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 2 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>replicated</th><th scope=col>0</th><th scope=col>1</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>0</td><td>95</td><td>78</td></tr>\n",
       "\t<tr><td>1</td><td>55</td><td>71</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 2 × 3\n",
       "\\begin{tabular}{lll}\n",
       " replicated & 0 & 1\\\\\n",
       " <dbl> & <int> & <int>\\\\\n",
       "\\hline\n",
       "\t 0 & 95 & 78\\\\\n",
       "\t 1 & 55 & 71\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 2 × 3\n",
       "\n",
       "| replicated &lt;dbl&gt; | 0 &lt;int&gt; | 1 &lt;int&gt; |\n",
       "|---|---|---|\n",
       "| 0 | 95 | 78 |\n",
       "| 1 | 55 | 71 |\n",
       "\n"
      ],
      "text/plain": [
       "  replicated 0  1 \n",
       "1 0          95 78\n",
       "2 1          55 71"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 计算不同水平的数量\n",
    "result_df2 <- df %>%\n",
    "  group_by(replicated, language_style) %>%  # 按 'replicated' 和 'language_style' 分组\n",
    "  summarise(数量 = n(), .groups = 'drop') %>%  # 计算每组的数量并取消分组\n",
    "  pivot_wider(names_from = language_style, values_from = 数量, values_fill = list(数量 = 0))  # 转换为宽格式\n",
    "\n",
    "# 显示结果\n",
    "result_df2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2574f385",
   "metadata": {
    "_id": "D7B1CA15338E40EC923C2CD12E25E9C3",
    "id": "8ACE15B0E4214BF8A86D726BE5BC0F1A",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
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    },
    "scrolled": false,
    "slideshow": {
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   },
   "source": [
    "### 先验 (prior) 和 数据 (data)  \n",
    "\n",
    "#### 先验  \n",
    "\n",
    "在我们这个事件中，我们评估某项研究可重复性之前，我们关于研究可重复性的信念，在贝叶斯统计中被称为先验（prior）。  \n",
    "\n",
    "假设我们的信念被2015年Science的文章所影响，相信约40%的心理学实验是可重复的。这就是我们开始了解这项研究前的信念。  \n",
    "\n",
    "- 先验（prior）：指没有观察到具体数据之前，根据已有知识、经验或主观判断对某个事件发生概率的初步估计。  \n",
    "\n",
    "本例中，40%的估计代表了我们基于已有文献和领域经验的先验信念——即在没有观察具体文章之前，推测它有40%的研究能够成功重复。  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59c453f4",
   "metadata": {
    "_id": "3AFE8BA367D04C728F6936BFE83C68D8",
    "id": "8510F6F814694D158D13B3A08811F75E",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
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    },
    "scrolled": false,
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   },
   "source": [
    "#### 先验 vs 数据  \n",
    "\n",
    "在了解到被评估的研究来自Herzenstein 等（2024）之后，我们又获得了新的信息，这个新信息我们将其称为数据（data）。  \n",
    "\n",
    "此时，我们会有两个信息：  \n",
    "\n",
    "- 先验信息 (prior)：约 40% 的研究是可重复。  \n",
    "- 数据 (data) ：有 56%能被重复的研究使用了确切的语言风格；约45%不能被重复研究使用了确切的语言风格。  \n",
    "\n",
    "我们会如何推断？"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffaf9fc8",
   "metadata": {
    "_id": "B32FEE0C2D57457A83455C875FB2E8E8",
    "id": "38E45E9401034D209F2599EA4B0BD999",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
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   },
   "source": [
    "在先验和数据之间找到平衡？  \n",
    "\n",
    "这正是贝叶斯的思路：基于数据对先验进行更新。  \n",
    "\n",
    "$$  \n",
    "Posterior = \\frac {data * \\, prior}{Average \\, probability \\, of \\, data}  \n",
    "$$  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjkvl0f6gx.png?imageView2/0/w/960/h/960)  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef7d41c5",
   "metadata": {
    "_id": "3CC4CAB875C945868176443036FE5CEF",
    "id": "1981F998E95F4132B166ED49ECA94AA0",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
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    },
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    },
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   },
   "source": [
    "#### 先验概率(Prior probability)  \n",
    "我们现在使用更加正式一点的语言来对上述的信息进行描述：  \n",
    "\n",
    "假如一项心理学研究**能**被其他研究者独立地重复出来，我们认为一个特定的事件发生了。  \n",
    "\n",
    "我们将这个事件使用$B$来表示。  \n",
    "\n",
    "假如一项心理学研究**不能**被其他研究者独立地重复出来，我们认为一个特定的事件**没有**发生了，使用符号$B^{c}$(B的补集complement)。  \n",
    "\n",
    "根据Science于2015年的文章，我们可以得以下公式：  \n",
    "\n",
    "$$  \n",
    "P(B) = 0.40 \\\\  \n",
    "\n",
    "P(B^{c}) = 0.60  \n",
    "$$  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "720ac14a",
   "metadata": {
    "_id": "84A1E61DCF1B49E3961E5D2DE1354729",
    "id": "BDF24AD9A3F44DC1B51F75FED304E021",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
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   "source": [
    "<style>  \n",
    "table {  \n",
    "    width: 100%;  \n",
    "    table-layout: auto;  \n",
    "}  \n",
    "</style>  \n",
    "\n",
    "| 事件       | **$B$**   | **$B^{c}$** | **Total** |  \n",
    "|------------|-----------|-------------|-----------|  \n",
    "| **probability** | **0.4** | **0.6**     | **1**     |  \n",
    "\n",
    "\n",
    "换一句话说，在我们对需要被评估的研究进行评估前，我们关于事件$B$的先验信念是$P(B)$，这也被称为先验模型(prior model)  \n",
    "\n",
    "作为一个有效的概率模型(valid probability model)，它必须：  \n",
    "\n",
    "（1）考虑所有可能的事件（所有文章都必须是可重复或不可重复的，没有其他可能性）；  \n",
    "\n",
    "（2）它为每个事件分配先验概率；  \n",
    "\n",
    "（3）这些概率加起来为1。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e687a62d",
   "metadata": {
    "_id": "194A3554CB3042419CEE8B257085C841",
    "id": "15789B51556D43DEBD61C978D1E91321",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
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   "source": [
    "### 数据模型（条件概率与似然性）  \n",
    "\n",
    "借鉴先验模型的构建方式，我们同样可以采用模型（即公式）对关于目标研究的新信息进行正式地描述。  \n",
    "- 我们用符号 $A$ 表示研究中使用了确切的语言风格。  \n",
    "\n",
    "我们要将如下一句话的信息进行形式化：  \n",
    "\n",
    "**有 56%能被重复的研究使用了确切的语言风格；约45%不能被重复研究使用了确切的语言风格。**  \n",
    "\n",
    "**有 56%能被重复的研究使用了确切的语言风格，44%的能被重复的研究没有使用确切的语言风格；约45%不能被重复研究使用了确切的语言风格；55%的不能被重复的研究没有使用确切的语言风格。**  \n",
    "\n",
    "将数据形式化，通过条件概率来量化文章展现出语言确切的可能性。具体如下：  \n",
    "\n",
    "$$  \n",
    "P(A|B) \\approx 56\\%  \n",
    "$$  \n",
    "- 当研究是可重复的，使用确切语言的概率大约 56%。  \n",
    "\n",
    "$$  \n",
    "P(A|B^{c}) \\approx 45\\%  \n",
    "$$  \n",
    "- 在研究不可重复的情况下，使用确切语言的概率大约为 45%。  \n"
   ]
  },
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    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjq96jfv8f.png?imageView2/0/w/960/h/960)  \n"
   ]
  },
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   "source": [
    "#### 条件概率  \n",
    "\n",
    "条件概率：给定某个条件下发生另一件事情的概率。  \n",
    "注意：条件概率的定义是有顺序的，$P(A|B)$ 与 $P(B|A)$ 并不相等。  \n",
    "\n",
    "例如：  \n",
    "- $P(A|B)$ 表示在研究可重复的情况下，使用确切语言的概率；  \n",
    "- $P(B|A)$ 表示的是在研究使用确切语言的情况下，该研究是可重复的概率。  \n",
    "\n",
    "很多时候，人们容易混淆这两者，尤其在贝叶斯推理中。因此，清楚条件的前提和结果是很重要的。"
   ]
  },
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   "source": [
    "#### 似然(likelihood)  \n",
    "\n",
    "**似然的定义**  \n",
    "\n",
    "从条件概率中，我们知道 $P(A|B) = 0.56$ 和 $P(A|B^c) = 0.45$，即使用确切语言的研究更可能是可重复的。  \n",
    "\n",
    "似然（likelihood）描述的是在不同假设下，某个数据模式出现的可能性。在这个例子中，我们比较两种假设:  \n",
    "- $P(A|B) = 0.56$：在可重复研究的假设下，使用确切语言的概率较高。  \n",
    "- $P(A|B^c) = 0.45$：在不可重复研究的假设下，使用确切语言的概率较低。  \n",
    "\n",
    "因此，似然函数表明：当前数据模式（使用确切语言）在可重复的假设下更可能出现：  \n",
    "$P(A|B) = 0.56 > P(A|B^{c}) = 0.45$  \n",
    "\n",
    "这就是似然函数(likelihood function)的核心：反映了在不同的假设（可重复或不可重复）下，某个数据$A$出现的可能性。  \n"
   ]
  },
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   "source": [
    "例如，针对“数据 A：研究使用确切语言”的似然可以写成：$L(*|A)$  \n",
    "$$  \n",
    "L(B|A) = P(A|B) \\quad\\quad L(B^{c}|A) = P(A|B^{c})  \n",
    "$$  \n",
    "\n",
    "上述两个式子分别表示在“研究可重复”和“研究不可重复”两种可能的情况下，使用确切语言的概率。  \n",
    "\n",
    "*注意，在似然函数中，数据是已知发生的，而假设是可能发生的"
   ]
  },
  {
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   "source": [
    "#### 概率(Probability) vs 似然(likelihood)  \n",
    "\n",
    "🤔概率和似然似乎都在表示某种可能性，它们的区别是什么呢？  \n",
    "  \n",
    "| 特性        | 概率 (Probability)                                      | 似然 (Likelihood)                                   |  \n",
    "|-------------|---------------------------------------------------------|----------------------------------------------------|  \n",
    "| 定义        | 已知假设条件，得到某个数据的可能性                           | 已知数据，不同假设条件下得到该数据的可能性     |  \n",
    "| 范围        | [0, 1]                                                 | 不限于 [0, 1]                                     |  \n",
    "| 总和        | 所有可能事件的总和为1                                  | 可以不等于1                                       |  \n",
    "| 应用        | 预测和决策                                           | 模型估计和选择                                     |  \n",
    "\n",
    "注意：  \n",
    "* 先验概率的总和等于1，因为先验表示所有可能结果的分布，表示事件B发生的概率，是我们的主观推测；  \n",
    "* 似然总和不等于1，因为似然函数不是概率函数，它告诉我们事件A在不同假设下发生的相对可能性。"
   ]
  },
  {
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    "根据我们的例子，概率和似然可以整理为下表：  \n",
    "\n",
    "TABLE 2.2: Prior probabilities and likelihoods of reproducible research.  \n",
    "\n",
    "| event       |     $B$     |     $B^c$   |   total   |  \n",
    "|-------------|--------------|--------------|-----------|  \n",
    "| prior       |      0.4    |      0.6     |     1     |  \n",
    "| likelihood   |     0.56    |     0.45     |   ≠ 1     |"
   ]
  },
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   "source": [
    "## 分母（normalizing constant）-- 边际概率 (marginal probability)  \n",
    "\n",
    "似然函数描述了在可重复性研究和不可重复研究中使用确切语言的情况。  \n",
    "\n",
    "我们想知道的是：所有研究中使用自信语言的总体可能性是多少。  \n",
    "\n",
    "这被称为边际概率 $P(A)$"
   ]
  },
  {
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   "id": "4bf14f6d",
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   "source": [
    "我们要做的，就是把每个假设下出现事件$A$的似然与每个假设本身的概率相乘（即把每个假设自身的概念纳入考虑），这两者之和即为边际概率。  \n",
    "$$  \n",
    " P(A) = P(A \\cap B) + P(A \\cap B^{c}) = L(B|A) * P(B) + L(B^{c} | A) * P(B^{c})  \n",
    "$$  \n",
    "\n",
    "$$ P(A) = 0.56 * 0.4 + 0.45* 0.6 = 0.494 $$  \n"
   ]
  },
  {
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   "source": [
    "### 后验概率模型(Posterior probability model via Bayes’ Rule)"
   ]
  },
  {
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   "source": [
    "**直觉理解**  \n",
    "\n",
    "最后，我们来计算后事件$B$的后验概率，即，当我们知道某个研究使用了确切的语言风格之后，它能被重复的可能性是多少？  \n",
    "\n",
    "我们同样通过条件概率来描述它：$P(B|A)$。  \n",
    "\n",
    "在正式计算之前，我们可以回顾一下这个表格来建立一些直觉。   \n",
    "\n",
    "||$B$|$B^c$|Total|  \n",
    "|---|---|---|---|  \n",
    "|$A$|0.56 * 0.4 = 0.224|0.45* 0.6 = 0.27|0.494|  \n",
    "|$A^c$|0.176|0.33|0.506|  \n",
    "|Total|0.4|0.6|1.0|  \n",
    "\n",
    "note：  \n",
    "- $A$ ：表示使用确切语言的研究。  \n",
    "- $A^c$ ：表示不使用确切语言的研究。  \n",
    "- $B$ ：表示研究是可重复的。  \n",
    "- $B^c$ ：表示研究不可重复的。  \n",
    "\n",
    "因为我们知道这项研究**使用确切语言风格**，所以我们直接锁定第一行，  \n",
    "- 在A行中，45.3%(0.224/0.494)的研究是可重复的，54.7%(0.27/0.494)的研究是不可重复的。  \n",
    "- 因此，根据后验概率 45.3%的可能性可以认为当前这一研究是可重复的。  \n"
   ]
  },
  {
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   "source": [
    "**正式计算**  \n",
    "\n",
    "如何凭借贝叶斯公式的数学形式推导得到该结果？  \n",
    "\n",
    "$$  \n",
    "Posterior \\sim P(B|A) = \\frac {data * prior}{Average \\, probability \\, of \\, data} ={\\frac{P(A\\cap B)}{P(A)}}={\\frac{L(B|A) * P(B)}{L(B|A) * P(B) + L(B^{c}|A) * P(B^{c})}}  \n",
    "$$  \n",
    "\n",
    "- $P(B|A)={\\frac{P(B)L(B|A)}{P(A)}}={\\frac{0.4\\cdot0.56}{0.494}}=0.453$  \n",
    "- 当带入之前计算得到的数值到贝叶斯公式中，我们得到了确切语言为可重复研究的概率。  \n",
    "\n"
   ]
  },
  {
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    "使用同样的方法，我们可以计算出使用确切语言的研究为不可重复研究的概率，结果如下表。  \n",
    "- 可以注意到：先验概率和后验概率的和均等于1。  \n",
    "\n",
    "TABLE 2.4: The prior and posterior models of reproducibility.  \n",
    "\n",
    "\n",
    "| event    | $B$     | $B^c$ | Total    |  \n",
    "| --------  | -------- | -------- | -------- |  \n",
    "| prior probability | 0.4 | 0.6 | 1 |  \n",
    "| posterior probability | 0.453 | 0.547 | 1 |  \n"
   ]
  },
  {
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   },
   "source": [
    "思考时间🧐：是否加入分母的意义何在？"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3887fb5",
   "metadata": {
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   },
   "source": [
    "#### 后验概率计算模拟练习  \n",
    "\n",
    "\n",
    "🤓为了深入理解先验知识、似然（数据）和后验概率，我们将通过编写代码来计算后验概率，以增强对这些概念的理解和实践能力。"
   ]
  },
  {
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   "source": [
    "1. 定义研究的可重复性与相应的先验概率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "a6eef0ac",
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   "source": [
    "# 定义文章类型\n",
    "article <- data.frame(replicated = c(\"yes\", \"no\"))\n",
    "\n",
    "# 定义先验概率\n",
    "prior <- c(0.4, 0.6)"
   ]
  },
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   "source": [
    "2. 模拟一些可能被投放给你的研究"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "fb921e55",
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    "_id": "5FE6653043FA4C9AB98D071433A517EC",
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    "id": "E38F6CBE358E439D97CF711B263487B3",
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   replicated\n",
      "1         yes\n",
      "2         yes\n",
      "3          no\n",
      "4         yes\n",
      "5         yes\n",
      "6          no\n",
      "7          no\n",
      "8          no\n",
      "9         yes\n",
      "10         no\n"
     ]
    }
   ],
   "source": [
    "# 模拟生成 10000 项研究，包括其类型\n",
    "set.seed(84735)\n",
    "article_sim <- article %>% \n",
    "  slice_sample(n = 10000, weight_by = prior, replace = TRUE)\n",
    "\n",
    "# 查看前 10 行数据\n",
    "print(head(article_sim, 10))"
   ]
  },
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    {
     "data": {
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gLgUSLgAeO3asPf/883HZGFQaAQQQQAABBBBAAAEEEEAgdgJxvQ9w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CvLRrHnnkkYIjjjgi7VhQTir4K5gxY0ba9anZi9POHTZsWFr+L37xi7T8r776Ki0/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\nIIAAAggggAACCCRG4P8BIA3GD/veJ5sAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#我们可以通过画图来查看这些被投放研究的可重复性比例。\n",
    "options(repr.plot.width=8, repr.plot.height=5) #自定义画布大小\n",
    "article_sim %>%\n",
    "  count(replicated) %>% \n",
    "  ggplot(aes(x = replicated, y = n, fill = replicated)) +\n",
    "  geom_bar(stat = \"identity\",width = 0.6) +\n",
    "  labs(x = \"replicated\", y = \"counts\") +\n",
    "  scale_fill_manual(values = c(\"yes\" = \"skyblue\", \"no\" = \"salmon\")) +\n",
    "  scale_y_continuous(expand = c(0,0),limits = c(0, 6000)) + \n",
    "  APA_theme"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8bbca1d",
   "metadata": {
    "_id": "A67F09F99463465D922E85F27AA61FAA",
    "id": "781F44A7CAFA406FB210290BEC0285FA",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "3. 接下来我们需要模拟10000项研究使用确切语言风格的情况，  \n",
    "- 和之前相同，不可重复研究使用确切语言风格的可能性为45% ，  \n",
    "- 可重复研究使用确切语言风格的可能性为56% "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "9c0cb6c8",
   "metadata": {
    "_id": "EDE9730D549649EAA93AD55395737CD7",
    "collapsed": false,
    "id": "747161B8FCE14DB68BB6BE5E322F597E",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# 设置条件概率\n",
    "article_sim$data_model <- ifelse(article_sim$replicated == \"no\", 0.45, 0.56)\n",
    "\n",
    "# 定义研究是否使用确切语言\n",
    "data <- c(\"certain\", \"uncertain\")\n",
    "\n",
    "# 生成确切语言相关的数据\n",
    "article_sim$language <- mapply(function(p) sample(data, 1, prob = c(p, 1 - p)), article_sim$data_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "003d1e60",
   "metadata": {
    "_id": "E1F09028FF044BED8FFB4AE3E0CB8988",
    "collapsed": false,
    "id": "E5CA81617B1043C49D98F743BE5F9F15",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A tibble: 2 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>language</th><th scope=col>no</th><th scope=col>yes</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>certain  </td><td>2604</td><td>2264</td></tr>\n",
       "\t<tr><td>uncertain</td><td>3365</td><td>1767</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A tibble: 2 × 3\n",
       "\\begin{tabular}{lll}\n",
       " language & no & yes\\\\\n",
       " <chr> & <int> & <int>\\\\\n",
       "\\hline\n",
       "\t certain   & 2604 & 2264\\\\\n",
       "\t uncertain & 3365 & 1767\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A tibble: 2 × 3\n",
       "\n",
       "| language &lt;chr&gt; | no &lt;int&gt; | yes &lt;int&gt; |\n",
       "|---|---|---|\n",
       "| certain   | 2604 | 2264 |\n",
       "| uncertain | 3365 | 1767 |\n",
       "\n"
      ],
      "text/plain": [
       "  language  no   yes \n",
       "1 certain   2604 2264\n",
       "2 uncertain 3365 1767"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 显示每个类别研究数量\n",
    "result <- article_sim %>%\n",
    "  group_by(language, replicated) %>%\n",
    "  summarise(数量 = n(), .groups = 'drop') %>%\n",
    "  pivot_wider(names_from = replicated, values_from = 数量, values_fill = list(数量 = 0))\n",
    "\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d10a2d5e",
   "metadata": {
    "_id": "DE820DB7BC9A4260A72A97A92D175958",
    "id": "BCB4367AB90649378E518B8CFEB7CE3A",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "4. 计算后验值  \n",
    "\n",
    "还记得我们的先验概率为：  \n",
    "- 可重复研究  $P(B)=0.4$  \n",
    "- 不可重复性研究 $P(B^c)=0.6$,  \n",
    "\n",
    "由以上结果可计算似然：  \n",
    "- 大约58.1%(2340/(2340+1687))的可重复性研究使用了确切语言, $P(A|B)=0.581$  \n",
    "- 44.2%的不可重复性研究使用确切语言(2643/(3330+2643)), $P(A|B^c)=0.442$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f21aa870",
   "metadata": {
    "_id": "491F9BD4FC4249B2A816ABEC734F72C5",
    "id": "B3788583403F48FD8E9185AAFAEC0F06",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "结合先验和似然，我们可以进一步计算分母(边际概率)：  \n",
    "- $L(B|A)*P(B) + L(B^{c}|A)*P(B^{c}) = 0.581*0.4 + 0.442*0.6 = 0.2324 + 0.2652 ≈ 0.498$  \n",
    "\n",
    "最后，我们可以计算得到的后验 (使用确切语言研究中，可重复性研究的概率)：  \n",
    "- $P(B|A) ={\\frac{L(B|A)*P(B)}{P(A)}}= (0.581*0.4)/0.498 ≈ 0.467$  \n",
    "- 在10000项研究中，使用确切语言的研究有4980篇(分母)  \n",
    "- 而现在，我们可以知道，在使用确切语言的研究中，47%(2340/4980)的研究为可重复研究"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "adad32fb",
   "metadata": {
    "_id": "463C518551694032AF27D25FB04F8AE7",
    "collapsed": false,
    "id": "C0DE035866FD4AD39D7F980DB28AD3C5",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "使用确切语言的研究： 4868 \n",
      "  replicated counts\n",
      "1         no   2604\n",
      "2        yes   2264\n"
     ]
    }
   ],
   "source": [
    "# 过滤使用确切语言的研究\n",
    "usage_yes <- filter(article_sim, language == 'certain')\n",
    "\n",
    "# 计算使用确切语言的总研究数量\n",
    "cat('使用确切语言的研究：', sum(table(usage_yes$replicated)), \"\\n\")\n",
    "usage_yes_count <- as.data.frame(table(usage_yes$replicated))\n",
    "colnames(usage_yes_count) <- c(\"replicated\", \"counts\")\n",
    "print(usage_yes_count)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cca6154f",
   "metadata": {
    "_id": "4F9AD7BE225841788D37CEEDC528748B",
    "id": "1569B8778BE44EF38DB13A131CBB1724",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "同样地，通过画图来可视化使用确切语言的研究的情况"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "4717c2d1",
   "metadata": {
    "_id": "0AEE39A369D24936AB824323E939DB11",
    "id": "7F4F99A182204E39B39398C9AE8A7FA7",
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nlm2nTTTbNt8SUnrgbMnTs3e73yyitT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\nAIHMChAAZ1aM8xFAAAEEEAiJQFJSkpo3b54tbfn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CCCAQCgEC4FBUM4VEAAEEEEAAAQQQQAABBBAgAOYeQAABBBBAAAEEEEAAAQQQCIUA\nAXAoqplCIoAAAggggAACCCCAAAIIEABzDyCAAAIIIIAAAggggAACCIRCgAA4FNVMIRFAAAEE\nEEAAAQQQQAABBAiAuQcQQAABBBBAAAEEEEAAAQRCIUAAHIpqppAIIIAAAggggAACCCCAAAIE\nwNwDCCCAAAIIIIAAAggggAACoRAgAA5FNVNIBBBAAAEEEEAAAQQQQAABAmDuAQQQQAABBBBA\nAAEEEEAAgVAIEACHopopJAIIIIAAAggggAACCCCAAAEw9wACCCCAAAIIIIAAAggggEAoBAiA\nQ1HNFBIBBBBAAAEEEEAAAQQQQIAAmHsAAQQQQAABBBBAAAEEEEAgFAIEwKGoZgqJAAIIIIAA\nAggggAACCCBAAMw9gAACCCCAAAIIIIAAAgggEAoBAuBQVDOFRAABBBBAAAEEEEAAAQQQIADm\nHkAAAQQQQAABBBBAAAEEEAiFAAFwKKqZQiKAAAIIIIAAAggggAACCBAAcw8ggAACCCCAAAII\nIIAAAgiEQuB/6OWpQQ3J9mQAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 计算所有语言的 replicated 值\n",
    "language_counts <- article_sim %>%\n",
    "  group_by(language, replicated) %>%\n",
    "  summarise(count = n(), .groups = 'drop')\n",
    "\n",
    "# 绘制图形\n",
    "options(repr.plot.width=8, repr.plot.height=5) #自定义画布大小\n",
    "ggplot(language_counts, aes(x = replicated, y = count, fill = language)) +\n",
    "  geom_bar(stat = \"identity\", position = \"dodge\",width=0.8) +\n",
    "  facet_wrap(~ language, scales = \"free_y\") +  # 创建子图\n",
    "  scale_y_continuous(expand = c(0,0),limits = c(0, 4000)) + \n",
    "  scale_x_discrete(expand = expansion(mult = c(0.65, 0.65))) +\n",
    "  labs(y = 'Count') + \n",
    "  APA_theme +\n",
    "  theme(legend.position = \"none\",strip.text = element_text(size = 16))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "448dec26",
   "metadata": {
    "_id": "E8021516E6B64E539FC5521887F739E6",
    "id": "306BCD1F559942D480905787A22618F5",
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### 总结 (Recap)  \n",
    "\n",
    "回到之前的问题：如何预测研究的可重复性？  \n",
    "\n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjq96jfv8f.png?imageView2/0/w/960/h/960)  \n",
    "\n",
    "\n",
    "\n",
    "- 哪些信念可以作为先验概率？  \n",
    "- 信息的哪些属性可以作为数据？  \n",
    "- 如何结合先验和数据更新信念 (贝叶斯公式)。  "
   ]
  },
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   "source": [
    "## Part3 随机变量的贝叶斯模型"
   ]
  },
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    "**随机变量 (random variables)**  \n",
    "\n",
    "在之前的分析中，我们讨论的是对某项研究的“可重复性”这样一个单一事件。  \n",
    "\n",
    "同样的逻辑可以应用于更加抽象和一般性的**随机变量**进行分析。  \n",
    "\n",
    "假设为了研究可重复性问题，一个有能力且资金充足的研究团队计划进行一系列可重复性实验，他们希望知道这些实验成功重复的比例是多少。  \n",
    "\n",
    "首先我们来了解一个概念，胜率或成功率  \n",
    "\n",
    "* 想象你玩斗地主，有五局三胜，七局四胜这一说，一轮玩下来，就会出现胜率。  \n",
    "* 然而，胜率并不是一成不变的，它会随着每次游戏的输赢而变化。  \n",
    "* 在每一轮开始前，你并不会知道你这次的胜率是多少  "
   ]
  },
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    "在我们的例子中，假设计划对6项研究进行重复实验。  \n",
    "- 假设该团队对于任何研究成功复现的成功率为$\\pi$，$\\pi$是**未知的且可能会变化**，所以$\\pi$是一个随机变量。  \n",
    "- 根据团队先前的经验以及心理学研究的现状，我们猜测其成功复现的成功率为 $\\pi = 50\\%$。  \n",
    "- 他接下来可能成功复现的次数$Y$可能是0，可能是1，也可能是6，可以有7种可能的成功复现次数，$Y \\in \\{0,1,2,3,4,5,6\\}$ "
   ]
  },
  {
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   "source": [
    "🤔虽然我们知道他们的平均成功率为 $\\pi = 50\\%$，但问题在于，对于每一种复现成功的次数（1 ～ 6），其可能性分别是多少呢？ "
   ]
  },
  {
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   "id": "31e4a1b6",
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   "source": [
    "**二项式模型**  \n",
    "\n",
    "由于每次重复实验，结果只有两种可能：成功 vs 失败。  \n",
    "\n",
    "该团队总共进行6次重复实验，我们想要知道的是成功1次，成功2次，成功3次，...，的概率。  \n",
    "\n",
    "对于这种情况，我们可以用二项分布来分析。  \n"
   ]
  },
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    "该团队的成功率为$\\pi$，$在\\pi$下某成功次数发生的概率可表示为：  \n",
    "\n",
    "$$  \n",
    "f(y|\\pi) = \\binom{n}{y} \\pi^{y}(1-\\pi)^{n-y} \\quad\\quad for\\;y \\in \\{0,1,2,...,n\\}  \n",
    "$$  \n",
    "$$  \n",
    "\\binom{n}{y} = \\frac{n!}{y!(n-y)!}  \n",
    "$$  \n",
    "\n",
    "$\\pi$ 表示成功的可能性，$y$表示在$n$个试次中成功的次数，二项模型含有的前提假设是：  \n",
    "\n",
    "(1) 所有试次发生都是相互独立的  \n",
    "\n",
    "(2) 在每个试次中，成功的概率都是一个固定的值$\\pi$  "
   ]
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   "source": [
    "成功次数为0~6 的可能性可以分别写成：  \n",
    "\n",
    "$$  \n",
    "f(Y=0|\\pi=0.5) = \\binom{6}{0} 0.5^0 (1-0.5)^{6}  \n",
    "$$  \n",
    "$$  \n",
    "f(Y=1|\\pi=0.5) = \\binom{6}{1} 0.5^1 (1-0.5)^{5}  \n",
    "$$  \n",
    "$$  \n",
    "...  \n",
    "$$  \n",
    "$$  \n",
    "f(Y=5|\\pi=0.5) = \\binom{6}{5} 0.5^{5} (1-0.5)^{1}  \n",
    "$$  \n",
    "$$  \n",
    "f(Y=6|\\pi=0.5) = \\binom{6}{6} 0.5^{6} (1-0.5)^{0}  \n",
    "$$  "
   ]
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   "source": [
    "我们可以使用代码帮助计算  \n",
    " `st.binom.pmf(y, n, p)`。其中 p 对应公式中的 $\\pi$。"
   ]
  },
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   "source": [
    "# 安装和加载包\n",
    "options(repos = c(CRAN = \"https://mirrors.tuna.tsinghua.edu.cn/CRAN/\"))\n",
    "if (!requireNamespace('pacman', quietly = TRUE)) {\n",
    "    install.packages('pacman')\n",
    "}\n",
    "pacman::p_load(\"tidyverse\",\"ggplot2\",\"dplyr\",\"car\",\"ggpubr\",'rstan',\n",
    "               \"BayesFactor\",\"bayestestR\",\"gridExtra\",\"TOSTER\")\n",
    "options(warn = -1)  # 抑制警告\n",
    "\n",
    "APA_theme <- theme(\n",
    "  plot.margin = unit(c(1, 1, 1, 1), \"cm\"),\n",
    "  panel.background = element_blank(), \n",
    "  plot.title = element_text(size = 14, face = \"bold\",hjust = 0.5,margin = margin(b = 15)),\n",
    "  axis.line = element_line(color = \"black\"),\n",
    "  axis.title = element_text(size = 14, color = \"black\",face = \"bold\"),\n",
    "  axis.text = element_text(size = 14, color = \"black\"),\n",
    "  axis.text.x = element_text(margin = margin(t = 10)),\n",
    "  axis.text.y = element_text(size = 14),\n",
    "  axis.title.y = element_text(margin = margin(r = 10)),\n",
    "  axis.ticks.x = element_blank(),\n",
    "  legend.background = element_rect(color = \"black\"),\n",
    "  legend.text = element_text(size = 13),\n",
    "  legend.margin = margin(t = 5, l = 5, r = 5, b = 5),\n",
    "  legend.key = element_rect(color = NA, fill = NA)\n",
    "  )"
   ]
  },
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     "name": "stdout",
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     "text": [
      " 成功次数     概率\n",
      "        0 0.015625\n",
      "        1 0.093750\n",
      "        2 0.234375\n",
      "        3 0.312500\n",
      "        4 0.234375\n",
      "        5 0.093750\n",
      "        6 0.015625\n"
     ]
    }
   ],
   "source": [
    "y <- c(0,1,2,3,4,5,6)  # 成功次数 \n",
    "n <- 6                # 重复研究总次数\n",
    "p <- 0.5              # 假设的成功概率\n",
    "\n",
    "# 计算概率值\n",
    "prob <- dbinom(y, size = n, prob = p)\n",
    "# 创建结果数据框\n",
    "result_table <- data.frame(成功次数 = y, 概率 = prob)\n",
    "\n",
    "# 显示结果\n",
    "print(result_table,row.names = FALSE)"
   ]
  },
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   "source": [
    "显然，当团队的成功概率为 0.5 时，其在六次研究中获得 *y* = 3 次成功的概率最高(*p* = 0.3125)。"
   ]
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    {
     "data": {
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IAAAQIECORJQACcp9HWVwIECBAgQIAA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\nQIAAAQIECBAgUJMCAuCaHFadIkCAAAECBAgQIECAAIFiAQFwsYh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4cGBWcnr2Ni2HVJzmz5+fPZvbo0ePbKmk4uMNbV999dVx5JFHRlr2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\nAkeTRqoAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制图形\n",
    "options(repr.plot.width=8, repr.plot.height=5) #自定义画布大小\n",
    "ggplot(result_table, aes(x = 成功次数, y = 概率)) +\n",
    "  geom_segment(aes(xend = 成功次数, yend = 0), color = 'gray', size = 1) +\n",
    "  geom_point(color = 'black', size = 3) +\n",
    "  labs(y = 'f(y | π)', x = 'y') +\n",
    "  xlim(-0.2, 6.2) +\n",
    "  scale_y_continuous(expand = c(0,0),limits = c(0, 0.5)) + \n",
    "  APA_theme  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe94a11d",
   "metadata": {
    "_id": "8041DF2125114C788A52694D4B45784E",
    "id": "30B1E04A446B4992A48DA9028E30F7AE",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "\n",
    "**概率质量函数(probability mass function, pmf)：** 用来描述离散型随机变量在各特定取值上的概率  \n",
    "\n",
    "在上图中我们看到，成功次数y在不同的取值上的概率不同。  \n",
    "\n",
    "* 由于$y$的个数是有限的，并且是随机发生的，我们把$y$称为离散型随机变量，而$y$发生的概率$f(y)$则被称为概率质量函数  \n",
    "\n",
    "\n",
    "对于离散型随机变量$Y$，$Y$各取值的概率由$f(y)$指定：  \n",
    "$$  \n",
    "f(y) = P(Y=y)  \n",
    "$$  \n",
    "\n",
    "并且有如下性质：  \n",
    "\n",
    "* 对所有y的取值来说，$0\\leq f(y) \\leq 1$  \n",
    "* $\\sum_{all\\,\\pmb{y}}f(y) = 1$，y取值的所有概率之和为1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "b4bb30b5",
   "metadata": {
    "_id": "05FC709EDC61405080FAEF84FC525F6E",
    "collapsed": false,
    "id": "734046F659A140CCAA1B6780E29C48FB",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1"
      ],
      "text/latex": [
       "1"
      ],
      "text/markdown": [
       "1"
      ],
      "text/plain": [
       "[1] 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sum(result_table$概率)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec9cfda9",
   "metadata": {
    "_id": "AA8EDB178D4B4E89A7544F8DE8489F30",
    "id": "DF201A487DBB411A89E51928FEF0B232",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### 二项似然函数(The Binomial likelihood function)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec374612",
   "metadata": {
    "_id": "49B4DD60B3174E9297B696DAEC178564",
    "id": "A52AEDE06598430085D53474BED4E44A",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "**不同的信念**  \n",
    "\n",
    "虽然我们认为该团队重复6个实验的成功率是50%，但并非所有人都这么认为。    \n",
    "\n",
    "- 乐观派认为该团队的成功概率为 0.8，表示对实验成功复现持高度信心。  \n",
    "- 悲观派则认为该团队的成功概率仅为 0.2，意味着对实验成功复现不太乐观。  \n",
    "\n",
    "成功的概率影响着他们对研究复现结果的预期：如果团队的成功概率高，那么6次研究中成功复现的次数会更多；  \n",
    "反之，如果成功概率低，那么研究复现的失败次数就会更多。  \n",
    "\n",
    "我们可以计算持不同信念的人心中，该团队在6项研究中成功复现的次数的概率分布并画图。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "8866d99c",
   "metadata": {
    "_id": "09496DE9C3554C5899C273188217941F",
    "collapsed": false,
    "id": "D75FE92EF3A246269A9B589AC0BC7762",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 成功次数 本团队_0.5 乐观派_0.8 悲观派_0.2\n",
      "        0   0.015625   0.000064   0.262144\n",
      "        1   0.093750   0.001536   0.393216\n",
      "        2   0.234375   0.015360   0.245760\n",
      "        3   0.312500   0.081920   0.081920\n",
      "        4   0.234375   0.245760   0.015360\n",
      "        5   0.093750   0.393216   0.001536\n",
      "        6   0.015625   0.262144   0.000064\n"
     ]
    }
   ],
   "source": [
    "# 定义成功次数和总试验次数\n",
    "y <- 0:6  # 成功次数\n",
    "n <- 6    # 研究总次数\n",
    "\n",
    "# 定义三种成功概率并计算似然值\n",
    "p_values <- c(0.5, 0.8, 0.2)\n",
    "likelihoods <- sapply(p_values, function(p) dbinom(y, size = n, prob = p))\n",
    "\n",
    "# 创建结果数据框\n",
    "result_table <- data.frame(\n",
    "  成功次数 = y,\n",
    "  本团队_0.5 = likelihoods[,1],\n",
    "  乐观派_0.8 = likelihoods[,2],\n",
    "  悲观派_0.2 = likelihoods[,3]\n",
    ")\n",
    "\n",
    "# 输出结果表\n",
    "print(result_table,row.names = FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "727677c5",
   "metadata": {
    "_id": "DC62F21B049746FDA1E4D7D3062A8A9F",
    "collapsed": false,
    "id": "CD0C1F54D18F402B98231092EE4D0ADB",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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TnwwAPH9CX43XffXXnf+96Xp+d3v/td\nnxQP9qzuc8AobhjLaw9236NxG71SPolyZtYTud/v9HzzzVe56KKLhkW655579nveKKNkPbD7\nVLROmTKlesyhhx46rOs6iAABAr0i0EwFUvlvwmi8+OMf/7jjecayjDEYzlheuxXvfnqlfBP5\nOFbvX/bYY49qWaX881Usx8/Zd7/73T5fJe9f+pB05QZj+2Q/CQIBAq0X2GyzzdKnPvWpFEME\ndkqILtG//vWvq8nNWmOn7CVaylq6pC9+8YvV7bGQteJOMcxdhKwwln9263+f/OQn827Txf2F\nS3m4wosvvjideOKJxe6mP2+55Zam45Yj7r333vlqDC942GGHlXdZJkCAAIE6gX/+859pgw02\nSL///e/r9qQUv89jiJhyiCG7vvOd76SsR0XKXgiUd43K8iWXXJKynqfpwgsvHJXzdcpJWnXf\nvVI+Of/889Npp51Wk/3loYZjqJ6PfvSjNcMt10TuZ+XnP/95Ov3002v2xvCOWYVUdVsMu5T1\nREovvPBCddsOO+yQsl7a+XrkwX333VfdZ4EAAQIERiYQ5ZGscj8fendkZ3L0WAi04t1Pr5Rv\nIn/G4v3L97///XTmmWfWZH9MSVB+rxM/Z5///OfTn//855p43r/UcHTtigqkrs1aNzZaAvHL\nMWsRWvPvJz/5Sc3pP/ShD9XsL+Jnw8DUxOullXiIRMVB8a/8h3U43HHHHR3HEZVdM2fOrKY7\n68abjj/++HTQQQel4qEZO//xj3+kE044IY8X48Vut9121WO6bSEbZif99a9/rd7Wvvvum1cK\nxouR8pxP3/ve91LMATCUEHMZFWGppZbKKxyj0rH+35ZbbllEyz9333336txj8bMaL0cFAgQI\nEGgsEM+veG4VIeYTOPzww1M29Gp69tlnU8xDEL/nP/3pTxdR8s8//elPKRsqtGbbaKzE8+Pl\nl18e8FSDlTEGPHiEO8fq2s3c9wiT3lPlk29/+9tVrpiXMb7D0bCk3KAlG165z8uS6kH9LJx9\n9tnVPTHP4lVXXZX+/ve/5w1pogxUhKxXX7r++uuL1bxcEpVKEWI+pnI6qpEsECBAgEBDgVNO\nOSV/33LXXXeladOm5b9f43fuxImvT+ueNflP2fDpDY/vlI1jVcZo5v7H8tpj/e7H+5fH00jf\nv0Sj6CJEg5usR18+d+QDDzyQPvvZzxa78nc65bixw/uXKk93L3Rlvyo3RWCMBa688sqarp3Z\nS5UhXzGG1speqA/5uDgmm6y38sgjj1SyFyxDPj4OiC7E2Uv1AY/NKksG3D/SnTF0XfbbNf/X\nzBB2We+fSvbwGtZQaJHWZr0H6rqdFXyqaY60f+UrX2nI8JnPfKYaL2vd2jBOt2zMKm+q95pN\nHl2JruNFiPkBijyOz+ylS7Grqc911lmnenwMFzOUEMMGFtc+8sgjh3KouAQIEOgZgfPOO6/6\nuzJ+Z8Z8LllPpH7v/2c/+1lN/Pnnnz8vj/R7QN2OKFsMNi9e9mK95hqNhrCrO23Tq+NR/sle\nalTiX1x7oDCc+x5q2ahXyid/+MMfar5DX/va12ro/+3f/q26/01vetOg38nywTGHUVG+iDkx\nyyHKqTHEY7E/aw1d3l3JKpSq+2KY3ayHUs1+KwQIECDwL4H6IeyyRqkNabKKperv1fjdG3Mi\nDRReeumlQd+D9Hd8s8/z+uOH+qyuP76Z9XYu30T6h/ruJ44ZinevlG/CZSzev8R83UXZJT6z\n0XXiUtUQ0xHEXKhFnJVWWqm6r1jw/qWQ6N5PPZCynwCBQKsEokfFNttskxZffPG02GKLpajZ\n//d///e8B0sMj9ZfiKHQvv71r6fsF3U+lMwyyyyTllxyyXx5jTXWyIdQy35N1RwePX/WWmut\n6r8YciabXDK//sILL5yiZ8wb3/jGtP/++1d7hmQVU2nXXXfNh9jIHvJp2WWXTdG7KlpRDjV8\n4xvfqF470vHMM8/kp4j7iPVieLfYGL28irRGGosQrZ932223PD3RfTabZyg3i5ak2bw3KXup\nVERt+Dlc7/qTRToiffU9iX7wgx9U033zzTfnh0UvmzPOOKN6imwOh+pyLGQvG6rHFPc83M9s\nIvOaczdaieFbomXWUP5lFUGNTtVw27XXXlvd/ra3vS1lLxOr6zG8UTlkcxqVVwdcjta52cTp\n1TjZy57qcjML733ve6vRfvjDH1aXLRAgQIDA6wL1Q3FF69ONN9749Qh1Sx/84AfT1ltvXd0a\nz/boiVuEaGFafqZNnTo1RcvFbC6aFMN8RdkiyiBRFopnazlEb9E4NsoP5RBD0sT2GG6sCP2V\nMWL/WJd/Brp2XD/KAdFSOp5b2QTEeZkvyn2TJk1KWWVF3jo6esIUYSj3HccMt2zUbuWT5Zdf\nfkhlkyjHlL9rhV+jz3LZJPbX91Qul0+iNfvDDz/c6DQNt62yyirV7XPMMUd1ORaiR1I5rLrq\nquXVtOGGG+Y/A7ExvgPnnntuzX4rBAgQIDA0gZ133rk68kQcGb/P43lXDrGeNSRIb37zm/Ph\nRuM9SFbRlN7znvek6667rhy1Znmoz/PywcN9Vg9Uxui08k14DOXdz3C94zjvX/717SuXb2JL\ns+9f4t3Lfvvtl3bccce8rJJVBv3rhP//fwxpnTXurW6LEQrqg/cv9SJduN69dWPujMDYCQyn\nB1I2X0Ale3lQrbXPfp3ULGfj/Vey4TX6JDqraKlkQ4HVxK0/Ntazlzo1PZKit0c53llnnVWZ\nPHlyzbZi/0477ZRPxJdVSjXcv9pqq1UiHUMJ/fXkyYYfa3iNIi1FS+PLLrusEpP0FdsbfWbj\nsVayyoGGyRqud6N0Z3PxDJiOSFvRYjt7SNfEzR6uNekrt1xtdE9D2RZGg4X6VlnNnD+r2Bzs\ntPn+bOiXmnvNhhHoc1z0SiqumRXS++zvb0NWIVc9Lo4/6qijKtmQBJXspWMleiNlY/RWspcv\n/R1eyYY2qDk+1gUCBAgQeF0gej+UywXxzI3euoOFrPFCze/Xci+MrOFGzb5sLPVK1hilZlvx\nTIhnTfRULUL0rC72Nfos91Zu9KwuzjPW5Z+Brp29xKhkf7wPeB9xb1GuK3p6D+W+R1I2arfy\nSbQSb5TPA2371re+VWTzgJ/llshxvsK6OCgbZrjm2lnjpWLXoJ/Z0HjVY7NKrWrZPfL+C1/4\nQnVf9OZr1MMoe9lZjRPLAgECBAj0FWi2B1KMzFJ+bmQNNmpOljWErWTTCtTEKcePsk+MKlLf\nS3g4z/PiwiN5Vg9Uxui08k14NPvuZyTe7Va+6dT3L8X3t9FnvPfJGs1Uf4622GKLPtG8f+lD\n0nUbaptJZb9JBQIERl8gesoceOCB+ZjncfZokfrOd74zn7S6mJQuxvKNGv+s8FKTgJhfJ1rw\nFiFazERrmexFSs2Yv+ecc07e6raIV/8Z45JmXbZT9FjaaKONao79xS9+kbc0yF5ipIUWWihP\nV/n4aFH8uc99rrxpTJdj8uHo+VRYRM+jrDCVsq606V3velfKXnjl189+I+ctJaJ1czmMxLt8\nnuEsX3755dXDwrJ+7qfqzi5YqG+x26jnUnlbfL+aDVmlXU3UQw45JB166KHpN7/5TT55dbSQ\niVYw9a2Mi4OiZXM5DNZbrRzXMgECBHpBIOZtiXJBEaJ3c/QQGiyU57eLuPU9icrHf/zjH0/T\np09P0XIxelxHz+sixNxK0asoG6Kk2DQmn60s/8S8O8VzKXqjRM/lgw8+OIXDyiuvXL2/KNfF\nM20oYaRlI+WT17XLZZPYOpTySUxcvcMOO+Qni3kxo6fZ+uuvn7dmjwm8I0Rvs+ilHr3n60O5\nfJK99EpRlhUIECBAYOgC8Tv4q1/9as2BMSJGOXzkIx9JMWdjEWIElniXEj2DI8T7hugl89Of\n/rSIkn8O93k+0md1TSIGWemW8k3c5nC941jlm1B4PZTLOEMp37x+hr5L2RDWNT37okd1fSiX\nb2Kf9y/1Qp2//vqMc51/L+6AQFsKRKEkhokrQlQqZGOzp2JYiwsvvDBtv/32+e4YRiPrKZS/\nUIkNMazdb3/72+LQFF1Jr7jiilRUOsUv8hjirQgx/FsM7dYoxDG//vWv07bbbpvvznpwpKyF\nZk3UrCdSioqoGCbkxhtvTNEFNmsNkscpXojUHDCMlfjjOgppUZEVkxdHiAfQBRdckC9nY8Kn\nm266qWaIu4suuiiVX1j96le/yivbYhi/qET43//933x4uzjBSLzzBDT4L14OPPfccyny561v\nfWs1RlRqfOlLX8rXi5cE8TKgCDEEYH2I/I4uwhFuv/32FIXaIsTkhFEQLELWcjVtttlmxWr+\nPSm/cIqhcAYLkYflLt2DxY/9kf/NhPoKpKgYrQ9ZC9zqpvr41R0NFuorkBpEyYdFigrFiBvf\np3KIl5XxXSqGCYrvb1Q6CQQIECDwL4GsV0YNRQwx10yISqAYhq54hkcjjqiIKhp3lM8RZYhd\ndtklr/iP52TE+9jHPlYduiuerYcffniKoUZjaN+oTIpJe6PBSBGyXkr5sHr1w4UV+wf7bGX5\np1xmiyFso7xShHjRFS+2brvttvyZFemKyoNm7zuGyi0P/zuUslGkod3KJ1lP8RQv2oYS1l13\n3aail8sbUaapL9eUyyZxwnL8wS4Q3//4TkZF0qmnnppHL7+cjIrDSy+9NG2++eYNT1UuG8bP\nYAzXm41C0DCujQQIECDwL4F4VxB/i8ew/PGOJIZ/jRfU2QguNUSbbLJJdX3KlCkpGyWkuh5/\nC373u9/NhxuNRixRkVTsj/cTMUxv8bwYzvM8nusjfVZXE9vEQruXbyJ9zbz7iVsdrncc227l\nm059/xKWjcIf//jHfMqNYl80aG/UuNz7l0Koiz+7rk+VGyLQAoGhDGGXFWyqXT2zXyX58Fv1\nScwqk6pxshfh9bsrjz76aCWrOKpEF+1yiKExskJO9djoIlyE+i7Oe+yxR7Er/4xzRnqKf9kv\n/D7D1GUtKqv7s3mHao4fbGWg7tdx7EATKca9FumKzxgeJ7qCxwSURYhutI3CSL0HSnfWE6sm\nXdlLrz5JyHpLVeNklXV99pc3ZHM/VePGfdZPthzD35UdshbM5cPHfTmGRSynrz79kcCs8q0a\nJ4YIaDZkhf/qcfEdzyrrKlklUCXyN6skre6L62fzdTScALs89GNW8dfspcUjQIBATwicf/75\nNb9LP/CBDzR93zG0bfn3/z333JMfWz+E3RJLLNFnGK8ou5TLAFlP3ZrrnnjiiTXnjt/79WGg\nZ/VYl38Guvbb3/72atqj3HTsscdWCpu4h3iuZ41I6m8nXx/svkdSNooL9FL5JOvtVc2HKN/W\nhxg6sfz9zV4c1kcZcP2www6rGcqlfK5YjjJHDJvUKGSVijXXzioCG0WzjQABAj0tUD+EXf3v\n2Ubr2QgvNc/YGPq2HO/++++vMc0aztbs//nPf17dP9zn+Uif1QOVMTq1fBOo5XJfeUjiAny4\n3nF8L5VvxvL9S5EX5c+sUXklm+O65uckazxTjlKz7P1LDUfXrTTXzDz7rSsQIDA8gWgpUw7R\nKqa+K2lWQVIdAiZ602S/aaq9jOLY6GIdPS0iZAWfFK0A4l8M5xUtWoswUEvO7KFcRMs/o3dG\nOUQPn/pt0cK4CNHSp1UhWuhG65/i3qJbcvyLFqMbbLBBeve73533pIreXPVhNLzrzzmU9Wz+\niGr0civT6sYWL0Tr1himaCghq+hJzbTyrW8NXvRWK1+rvK3cnbocp9HyaaedlvfQip+HyPMY\ndrEIMfxjTPKezcORb7r++uvzFt3RU6wcwr8Y/rG+pX05nmUCBAj0okAMD1sODz30UHl1wOWs\nQUt1f/S4iMmoG4WYULfooVvsj/XoeZ2NEZ9vil5I8eyMnjhjEVpZ/olnVfQyjxATDMcwxPEv\nhvXIxovPyy5Rnqt/fjZz3yMpG8X52618klU2VntkN3P/ESe+s9H7fLBQ9i2XQ4rj6rfVl3+L\neI0+Y5idmOS8CNF7P6t8Tc8880ze0jrKoX/5y1/yIRujJ1L9cEr1ZUPlk0LSJwECBIYvEH8f\nRu/Q8u//8nuBtdZaK99Xfg8Tf+/GkKPF6CDl+MN9no/0WT0UgW4p38Q9D9c7jm238k2nvn8J\ny3KI3nnRSy966xUhRj/K5qMuVvt8ev/Sh6SrNqhA6qrsdDPtKFAuiET6YuiWgUL8URsPnfKL\nlBiiK4acy3rhpIFe8MRLnP5C/R/HUVgqh+iKWh8aDUlWH2cs1rNWu/lwNjFnQDm8/PLL+dwC\nMRxZDG/zlre8Jf9jPV7KFGE0vItzDfUzXhaV55Oofzk31PONRvwYMu8Tn/jEkE4Vw7PEC73B\nQnRTLofyvRfbyxWPSy21VLF50M9VVlklxb/+QsybUVQgRZwYAqZRBVJxfLlgWWzzSYAAgV4W\nqB8GtdnGBjFsTPmPyRVWWCFv4NHIMvY1CvXPx7vvvrum3NPomOFua2X5J4a1jbJa/ZA60fjn\n9NNPz//FUH8xhHAMSZu16mz6tkZSNmrH8knMDzVQmbYRzLe+9a30n//5n4121Wwrl0/ixWB9\nw6xy2SQOHEr5JOspVr1WzEd63nnnVdejgVN8t2OIpRhCN4Y6znrQVffHQn0FkvJJDY8VAgQI\nNBSIuYuKZ2ZUEsWzNBonxvC7u+66az4XXfnA+Fs2G3GluimGjx3sd335mTTc5/lIntXVxDa5\n0C3lm7jd4Xq3Y/mmU9+/lL921113XV55FFMqFGHnnXfOh5mOoQn7C+UyjvJNf0qdu73/t82d\ne09STqCtBOKhNtRQLrzEeL8xR1D0yCi2R4EpemBkQ2jUvLSJniP9hUZzE5TjjldlUTkN5eW9\n9torZcPr9CkMluNE69WYF+riiy+ubh6pd/VEw1goekwVh5ZfYBTbuumzmHy0uKfyC8VG2wYr\ntBfHNPPZ6OVj/XFRgC/CQD8bRRyfBAgQ6CWBaCywzDLLVG85XrRkw61V1/tbKHrYFPuLOR2L\n9fJnNPxoFOp/J8cL/rEKrSz/xMusq666Ku27777VF1319xWNLWJOgK233rra07o+Tn/rwy0b\nKZ+83no2bOvLK82WT+LnIxuarpo9Mb9XOURPvJj7oAjxAqa+t1O5bBLx6n8WimN9EiBAgMDr\nAieccELKhn/P/8VczVdffXX+ruD4449v+L5gpO8ERvI8H+6z+vW7bW6pm8o3w/VWvqkt38Q3\np1zGabZ8U/7GNao8yqbDyOdKL/fwKx9TLJfLOMo3hUr3fKpA6p68dCdtKlDf+jaGs4hhuQb6\nl80tkN9NTCa94447Vnu1ZGO65xPzRqvG6FJ6xBFH1Nz1QD2QBmopECcZbH/NhVq0EkPc3HTT\nTfkQbNHiM4YJqa+0iKREK94ijMS7OMdwP6MVUDHxZpwj8q+bw2Ct159++unqJOvh0MywM4VX\ntN6Nl5kxDExRcVrsi8/4GSiHRueO6xehUQ+7Yp9PAgQI9KrAOuusU731qMSJFqADhYjzla98\npSbKm9/85pr18soDDzxQXq0u1/9ej/LNWIXByjeD7R9qurJx/vNe41EGiOF3o8fMeuutV1M+\niHPGUMTZ/DdDPX0+/N9Qy0bKJ7VD+UaPt3JoVIYo7y+WI8/Kob4xS+wryvCx/Nprr/Upr5TL\nJhFH+SQUBAIECIyuQPxeL4+4Ej1EB3r/EvtOOumkmkSM5Hk+nPcYNRdvYmWw8stg+5u4RE2U\nkXjUnKifleGcX/mmtnwzkvcvkS3RQDuGrSv3PPrsZz+b9zxqpkKoXMZRvunni97Bmw1h18GZ\nJ+mdIbDSSivVJPSJJ57IW52WN15zzTV5N+w11lgjlWvtr7zyynwYjCJuDN0RLVaLEK0Lyq17\nR7uQUFxnLD7LlV3xB3Y5RGvNGErnzjvvTNOnT0/ZZJLVfxEvKs8+9KEPpWIOhttvvz13inOO\nxLuchuEsh388KIvu8u1QgRRdjWPeraGEZr9HMYxADCdQvIj505/+VM2HuF59K/Vm5lWK42I4\nunipWbQo2nbbbfu8ZKt/ibP66qvHoTUh5iMoQhRIBQIECBCoFfja176WN0yJSvsIMRxXvGSJ\nYULrQ1QeHX744enWW2+t7oq5EgcaUiwqSOKP0HKP3LhWlG+KEPuWWGKJYjWVywexsb6MUI3Y\nhgsxvF+UXeLfmmuumbbccsv8XyQ1yn8xd060oi7CtGnT0g477JCvDnbfIykbtWP5JIYjLp7z\nhcdgn80+y+vLG1HhVq4sLZdP4rvX3xxe9empL2NGT/koo5RDuVd8tKguD0kd8cplk1hv9p4i\nrkCAAAECzQnEMzUalhbD28ffq9FYpfx3bjyX43kQz+uIW34OD/d5PpJndXN3Nj6xhutRpLZs\n26hcN9zzt2P5phPfv0Q+ReVPNNguVx7tt99+6bvf/W6RjYN+lss4yjeDcnVcBBVIHZdlEtxp\nAvGHZbSMKHpMxMuaqNWPbRGioiQqhYqKoJgM8frrr88LN+VhMiJuPFjLIV7klEMxAWR5W7su\nl7u/xvio8WIqCgDxYunDH/5w+vnPf15NegyvV56sLypE4g/yogIpJqcuCiUj8a5ecAQLUaHS\nThVIUclTjBc9gtvq99BoXRUVmxGiRfkZZ5yR51V8F8ut1OMlSnR9LkIMK/DJT36yWM1/BooX\nllGRGt2ti5brv/nNb/I5JYrK0+iVdPLJJ1ePjbmP6iepjp3lFu5rr712Nb4FAgQIEPiXwFvf\n+ta8gUbMsxghnsUxV2PM2xLP3ZhrMH6f33zzzSmGibniiiv+deD//3/UUUelqETqL0S5Jeb7\n+dGPflSd2PrYY4/NK1iKY973vvcVi/lnuXwQG4rGGFE+KJ71NQe0yUo0foiXUEWI8kDMuTDn\nnHPmm8IpJvkuVyDF3A1FGOy+R1I2imu0W/lkLHudRTk7PIvh4+Llxwc/+ME033zzpV/96lcp\nGrwUIV6OlHuPD1Q+id520QK3ePkVw0xHWSfKoRGivBINn4rQqHdeuWwS8ZRPCi2fBAgQGF2B\n3XffPX35y1/OT1r0MIohZosQcyqfeuqp+ercc8+dfvrTn+a9fEfyPB/ps7pIWzt9jsSjuI9y\nGaf+3c8dd9wxovJTu5VvOvH9S+RTlNfL86FGmSka6ZbfuxT5GeXx+vnKY1+5jKN8U2h1z6cK\npO7JS3fSpgLxizd+GX/961/PUxiFl/hlGj1o4g/bqCgpKo8iwkc+8pFqy5j6PzxjMt54qR6T\n08VxMc5+OTz55JPl1bZejhYJRQVQmETL0GgF9IMf/CAdeOCBeSvoeJEVIfzij/ItttgiPfLI\nI/mYx/EyqwhRiVGEkXgX5xjJZ0yoHBWAEYr7G8n52v3Y6NIc3f1ffPHFPKkx5vO3v/3tvBKt\n/H381Kc+lWK+jSLEd37KlCnFal4hWFQgxcbPfe5z6YADDsj3x/cgWsTHz03M1xHf+/LPzDe/\n+c0+LxXjmKlTp1bPv/7661eXLRAgQIDA6wLRKyZ6Tdx3333VjWeddVaKf9Gwo3gWV3f+/8Jm\nm23W8I/H+ng//vGPU/Q2iYr+aAkcjQCKEJUr8Tu8HOpbLEYv5Kh0iRf39b1Py8eN93I0foiG\nDpdddlmelGjtHBV022yzTT7Jd7RyjmGMixA9zjfffPNitU9PlPr7HknZKC7SS+WTaKT16U9/\nOn3ve9/LfePlVwxntMoqq6Rbbrmlah4vDPfee+/qeiwMVD6JBk37779/XpkacaOcE2WTyMco\nB5XL5fGzU5T9I24Ryj34Ik3lCaeLOD4JECBAYOQC0UAg5hws5kOK9fg9Hc/m+Hs9hpktQowi\nEo0PIozkeT7SZ3WRnnb6HIlHcR8Dvft573vfO6LyUy+Vb8JzLN6/xByP55xzTpFd+edzzz2X\nz+lZs/H/VxpVIHn/0kiqy7ZlmSwQIDBEgWzolajZqP7L/kgd8AxZ691K9gdqNX752PJy1uq3\nkrVqrJ4rG9qjstFGG/V7XNa6oZK1dq3uz4bgqB5/9tlnV7fHNbJhZKrnLRbK184mAi42Vz/f\n//73V8+RtRqpbm9mIXvxUT02rpNVDtUclrUGqtlfpCWb6yiPl7VWrmR/fDeMU8SNzw022KCS\n/bFfc+7hesdJBkp31jqmJj1ZD7Ca68ZKVhCtxslatFayAmufOMWGbCLQaty4l6yAW+zKP+PY\n8r1mrTxq9rfLStaat5INQVST1nK64zua9cqqSW7W8qgmflZJWLM/VnbbbbeaOOVzxnI2rnUl\ne8HZ57jYkLWeqTk2e2HTMJ6NBAgQIFCpZENOVD7xiU/U/N6s/51brMfv3uzFeCVrBNOHLhs7\nveYcWcOPStZ4oGZbcZ6sQqiS9Xzqc47sD9ZK9mK/zzHZy4dq3IGe1WNd/hno2lmPq0rWIKZP\n2ot7Lj6jfJP1XqneTyw0c98jKRv1WvkkylBbbbVVv3mRvfyoZD2TavIgVgYrn0TZPL7XRV72\n95k1+upz7tiQNRSrHpsNX9gwjo0ECBDodYGsIWH1d2X8ns0augyLJBvCtBLvSPr7XR3bF1po\noUr8XV4OI3mej+RZPVAZo1PLN+E62LufkXj3WvkmPEf7/Uu81xroZ6R+X5Sh6oP3L/Ui3bc+\nW/ZFEAgQGGOB6LIbvTSii3S04KifgC6GMInhY0477bSanhQRL4bayF6k16QwtkePjL/+9a/p\n0EMPre6LLqPRyrcTQrTO2W677WqSGvMgZL9m820xvNnVV1+dt9yNVpz1IYawi+F0Ik55gsyI\nN1zv+msMZz2r8KvO9RBj+1933XXDOU1HHRPzN0TL6hjqKFqjFCFalsd3N1qML7744sXmpj+j\n9ftPfvKTPq1zI7+jR1G0IIthAhqFmO+gCG9605sMEVNg+CRAgEADgegNE0NU/Pa3v817+zb6\nnR09JaKVaAz/FUPClIf9anDKfNO73vWuFL+P64exiLlk4lrloWSKc0Rv1fjdXz/8avQwLoYO\nK+K222cMUxflsCOOOKJmXqcinVGeiaF2oxd1/dB9zdz3SMpGvVY+ie9L9F4/+OCDUwyjWw7L\nLbdcvi9a8Q41RBn8kksuyecEqJ/fKM4VQ+lET7Mjjzyy4anL5ZOYJ0EgQIAAgbETiL8Zs8qh\nfGi6rKKo5kLx+3zXXXfN/46NXknlMJLn+Uie1eU0tNPySDziPgZ79zOS8/da+SY8R/v9y403\n3hinHVEol2+8fxkRZdsePCHqxNo2dRJGoEsFXnrppbzy5/nnn08rZBM2lufw6e+WY3i3mJQ5\nXtDHcG8xjEY3hJgvKIYWiQmMY2iRcgVEcX/R7TzGlI8KsnjJFWbxcqtRxVJxTPlzON7l44e6\nnLXiro6nHJOLF3MEDfU8nRg/ujrH8ETxsibmgiiPdzyS+3n44YfzoY/iex9DOxZzSvR3zphv\nKV5ARojhkb70pS/1F9V2AgQIEGggEPMXTZs2Lf89Hr/P6yt0GhySDw8WjQmKcPTRR+cv8GM9\n5jKK88V46jF012Ah5l6K8kGUAaICqr4SYLDjx3t/VHbFsyvKLzEhcVTARXlvsPJbs/c9nLJR\nr5ZP4s/dGC45hoGOeRMbVZAO5/sS83Ldf//9KYYrjMYt8d1uVKlUnDvmNo3K0whRno0y8GDf\nh+JYnwQIECAwcoF4JsecOzFkXfw+bqZsM9zneaR2OM/qkd/l2J5hJB7NvPsZzvl7tXwTOT1W\n71+G+i3y/mWoYp0XXwVS5+WZFBMg0OYC0cppvfXWy1MZL9LK8zW1edK7InnxomiJJZZIMUFn\nVEjGvB7mGOiKrHUTBAi0uUDML9NfBVKbJ70nkqd8Mr7ZHKMRFL3uYvLpU045ZXwT5OoECBAg\nQKALBJRvxjcTvX8ZX/9WXf31sYZadUXXIUCAQJcLrLvuuvkQa3Gb2XwQec+xLr/ltrq9a665\nJq88ikRl83ipPGqr3JEYAgQIEBgvAeWT8ZL/13WnTJmSL0Tjlmzux/FNjKsTIECAAIEuEVC+\nGd+M9P5lfP1bdXUVSK2Sdh0CBHpKoDxsXcwrIbROIJu4NL9YDCcTwycJBAgQIECAwL8ElE/G\n55tw++23V+fF/NjHPtZnXrDxSZWrEiBAgACB7hBQvhm/fPT+ZfzsW3llFUit1HYtAgR6RmCT\nTTZJxeTIp512Wor5roSxF4j5DX75y1/mF4rWvSuvvPLYX9QVCBAgQIBAhwgon4xPRn3nO9/J\nLzzvvPOmb3zjG+OTCFclQIAAAQJdKqB8Mz4Z6/3L+LiPx1UnjsdFXZMAAQK9IHDsscfmkyTH\nvcZE4Ouvv34v3Pa43mM4xwSOEyZMSIcddti4psXFCRAg0GsCb3zjG9NVV11VvW2V+FWKtlpQ\nPmltdsyaNStFr+i99torbbrppvk8ja1NgasRIECAAIHuF1C+aX0ee//SevPxuuKEbLKrynhd\n3HUJECBAgAABAgQIECBAgAABAgQIECBAgAABAgTaT8AQdu2XJ1JEgAABAgQIECBAgAABAgQI\nECBAgAABAgQIEBhXARVI48rv4gQIECBAgAABAgQIECBAgAABAgQIECBAgACB9hNQgdR+eSJF\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAIFxFVCBNK78Lk6AAAECBAgQIECAAAECBAgQIECA\nAAECBAgQaD8BFUjtlydSRIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAYVwEVSOPK7+IECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAgfYTUIHUfnkiRQQIECBAgAABAgQIECBAgAABAgQIECBA\ngACBcRVQgTSu/C5OgAABAgQIECBAgAABAgQIECBAgAABAgQIEGg/ARVI7ZcnUkSAAAECBAgQ\nIECAAAECBAgQIECAAAECBAgQGFcBFUjjyu/iBAgQIECAAAECBAgQIECAAAECBAgQIECAAIH2\nE1CB1H55IkUECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAgXEVUIE0rvwuToAAAQIECBAgQIAA\nAQIECBAgQIAAAQIECBBoPwEVSO2XJ1JEgAABAgQIECBAgAABAgQIECBAgAABAgQIEBhXARVI\n48rv4gQIECBAgAABAgQIECBAgAABAgQIECBAgACB9hNQgdR+eSJFBAgQIECAAAECBAgQIECA\nAAECBAgQIECAAIFxFVCBNK78Lk6AAAECBAgQIECAAAECBAgQIECAAAECBAgQaD8BFUjtlydS\nRIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAYVwEVSOPK7+IECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAgfYTUIHUfnkiRQQIECBAgAABAgQIECBAgAABAgQIECBAgACBcRVQgTSu/C5OgAAB\nAgQIECBAgAABAgQIECBAgAABAgQIEGg/ARVI7ZcnUkSAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQGFcBFUjjyu/iBAgQIECAAAECBAgQIECAAAECBAgQIECAAIH2E1CB1H55Mq4pOvroo9M7\n3vGONH369HFNh4sTIECAAAECBJoVUH5pVko8AgQIECBAoF0ElF/aJSekgwABAgQGElCBNJBO\nD+6788470+9///v04osv9uDdu2UCBAgQIECgEwWUXzox16SZAAECBAj0toDyS2/nv7snQIBA\npwioQOqUnJJOAgQIECBAgAABAgQIECBAgAABAgQIECBAgECLBFQgtQjaZQgQIECAAAECBAgQ\nIECAAAECBAgQIECAAAECnSKgAqlTcko6CRAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQItElCB\n1CJolyFAgAABAgQIECBAgAABAgQIECBAgAABAgQIdIqACqROySnpJECAAAECBAgQIECAAAEC\nBAgQIECAAAECBAi0SEAFUougXYYAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg0CkCKpA6Jaek\nkwABAgQIECBAgAABAgQIECBAgAABAgQIECDQIgEVSC2CdhkCBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAQKcIqEDqlJySTgIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAiwRUILUI2mUIECBA\ngAABAgQIECBAgAABAgQIECBAgAABAp0ioAKpU3JKOgkQIECAAAECBAgQIECAAAECBAgQIECA\nAAECLRJQgdQiaJchQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECHSKgAqkTskp6SRAgAABAgQI\nECBAgAABAgQIECBAgAABAgQItEhABVKLoF2GAAECBAgQIECAAAECBAgQIECAAAECBAgQINAp\nAiqQOiWnpJMAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg0CIBFUgtgnYZAgQIECBAgAABAgQI\nECBAgAABAgQIECBAgECnCKhA6pSckk4CBAgQIECAAAECBAgQIECAAAECBAgQIECAQIsEVCC1\nCNplCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQKdIqACqVNySjoJECBAgAABAgQIECBAgAAB\nAgQIECBAgAABAi0SUIHUImiXIUCAAAECBAgQIECAAAECBAgQIECAAAECBAh0ioAKpE7JKekk\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECLRIQAVSi6BdhgABAgQIECBAgAABAgQIECBAgAAB\nAgQIECDQKQIqkDolp6STAAECBAgQIECAAAECBAgQIECAAAECBAgQINAiARVILYJ2GQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIBApwioQOqUnJJOAgQIECBAgAABAgQIECBAgAABAgQIECBA\ngECLBFQgtQjaZQgQIECAAAECBAgQIECAAAECBAgQIECAAAECnSKgAqlTcko6CRAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQItElCB1CJolyFAgAABAgQIECBAgAABAgQIECBAgAABAgQIdIqA\nCqROySnpJECAAAECBAgQIECAAAECBAgQIECAAAECBAi0SEAFUougXYYAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAg0CkCKpA6JaekkwABAgQIECBAgAABAgQIECBAgAABAgQIECDQIgEVSC2C\nLl+mUqmkBx98MM2YMaO8edSXH3vssfT444+P+nmdkAABAgQIEOg9AeWX3stzd0yAAAECBDpd\nQPml03NQ+gkQIEBgvAVUILUwB/7+97+nD37wg2meeeZJyy67bJp//vnTBhtskI466qgUhZrR\nDGeddVZafPHF0/LLLz+ap3UuAgQIECBAoMcElF96LMPdLgECBAgQ6AIB5ZcuyES3QIAAAQJt\nITCxLVLRA4m47bbb0sYbb5yeeeaZ/G5XWWWVFD2Ebrrppvzf7bffnk4//fQ0ceLIs+S+++5L\n++23Xw+oukUCBAgQIEBgLAWUX8ZS17kJECBAgACBsRBQfhkLVeckQIAAgV4V0AOpBTn/yiuv\npG233TavPFprrbXSvffem+666670xBNPpDPOOCOvNIoeQ4cddtiIUzNr1qy0++67p2effXbE\n53ICAgQIECBAoHcFlF96N+/dOQECBAgQ6FQB5ZdOzTnpJkCAAIF2FVCB1IKcOfPMM9P999+f\nZptttnTppZemFVZYIb/q7LPPnvbYY490/PHH5+snn3zyiOdFOvroo9P111+f5pprrhbcmUsQ\nIECAAAEC3Sqg/NKtOeu+CBAgQIBA9woov3Rv3rozAgQIEBgfARVILXCPXkYRtthii7TMMsvk\ny+X/osfQpEmT0lNPPZXOOeec8q4hLf/lL39JX/3qV9MCCyyQDjnkkCEdKzIBAgQIECBAoCyg\n/FLWsEyAAAECBAh0goDySyfkkjQSIECAQCcJqEAa49yK7tNRsRNh1113bXi1qPDZcsst830X\nXnhhwziDbXzxxRfTbrvtll599dV04oknNqyoGuwc9hMgQIAAAQIEQkD5xfeAAAECBAgQ6DQB\n5ZdOyzHpJUCAAIFOEFCBNMa5NG3atPTyyy/nV1lppZX6vdqKK66Y7/vb3/7Wb5yBdvznf/5n\nuvPOO9Muu+ySPvShDw0U1T4CBAgQIECAwIACyi8D8thJgAABAgQItKGA8ksbZookESBAgEDH\nC0zs+Dto8xt4/PHHqylcZJFFqsv1CwsttFC+6cEHH6zfNej6xRdfnH74wx+mpZdeOv3gBz8Y\nNH45wtNPP53uvvvu6qZnn302n6upusECAQIECBAg0HMCyi89l+VumACBMRSoVCrpySefTJMn\nT07zzDPPGF7JqQn0toDyS2/mf4zIM2PGjBTv1SZMmNCbCO6aAAECYyigAmkMcePUUSFThIUX\nXrhY7PNZVCC99NJLadasWU1X4jz22GNpr732yh+Sp59+elpwwQX7nHugDf/zP/+TPv3pT9dE\nmXPOOWvWrRAgQIAAAQK9JaD80lv57W4JEBgbgalTp+Zz1F566aUp/s6LsOSSS+Z/v33hC19I\nb3jDG8bmws5KoEcFlF96J+Ofe+659K1vfSuddtpp6aGHHspvPN5lbb311unwww9Pb3nLW3oH\nw50SIEBgjAVUII0x8AsvvFC9wkCVO/PPP381XvxxMffcc1fXB1qIyqOoRNpvv/2q8ygNFL9+\n33LLLZc+/vGPVzdfcskl6d57762uWyBAgAABAgR6T0D5pffy3B0TIDC6AieccEKKYcZnm222\nNHPmzOrJH3nkkXTcccelU045JV1xxRVp7bXXru6zQIDAyASUX0bm1ylHx1CF73rXu/KencWU\nEZH2WI4Rei666KJ0zDHHpM9//vOdckvSSYAAgbYWUIE0xtlT7nX0/PPP58MWNLpk7IsQ3W1j\naINmQgxbFw/H1VZbLR177LHNHNInzsorr5yi9VsRYg6ma665plj1SYAAAQIECPSggPJLD2a6\nWyZAYNQEzj777PxvrBhZIv7Vh3jJGUNtvfOd70y33XZb3iupPo51AgSGLqD8MnSzTjsiGlDH\n784nnnii4e/X1157Lb+lQw45JMX34WMf+1in3aL0EiBAoO0EZmu7FHVZgpZaaqnqHcW41/2F\nYt+8887b1PB1d955Z96ibeLEiemss85Kc801V3+ntp0AAQIECBAgMCQB5ZchcYlMgACBqkAM\nobXPPvvU9Dqq7iwtRMVSNCIsN+Yr7bZIgMAwBJRfhoHWYYd88YtfTM8880zDyqPyrUTPzxip\n56mnnipvtkyAAAECwxDQA2kYaEM5ZKgFmGIupMGu8c1vfjPFRIER/7DDDusTvRgDNlq3xRiw\nEXbeeed8vO0+kW0gQIAAAQIECJQElF9KGBYJECAwBIFf/vKX6dVXX23qiFdeeSVNmTIlxcgS\n0ZBQIEBgZALKLyPza/ejZ8yYkaKHZ7O/Y6Oi/rzzzkuf/OQn2/3WpI8AAQJtLaACaYyzZ7HF\nFkuzzz57im60RaVOo0sW+9ZZZ51Gu/tsK8Z5jZ5Ll19+eZ/9xYZ4YBb7ja9dqPgkQIAAAQIE\nBhJQfhlIxz4CBAj0L3DDDTekmNN2KOHmm29O73jHO4ZyiLgECDQQUH5pgNJFm2655ZZBex6V\nbzd+F1933XUqkMoolgkQIDAMARVIw0AbyiExaeq6666bbrrppnT++eenHXfcsc/h0Yrisssu\ny7dvsMEGffY32hDjuG688caNduXb/vjHP6af/exnaY455kjf/va3823//u//3m98OwgQIECA\nAAEChYDySyHhkwABAkMTiPk5hhJiSHJDLA1FTFwC/Qsov/Rv0w174ndlvOMq5jlq5p7++c9/\nNhNNHAIECBAYQEAF0gA4o7XrwAMPTLvuumu64IIL8nGu64cnuPDCC9Nzzz2Xz3200047NXXZ\nGJauGJqu0QFxjahAij9IPvOZzzSKYhsBAgQIECBAoF8B5Zd+aewgQIBAvwLLLbdcdQSKfiOV\ndsRQTEsssURpi0UCBEYioPwyEr32PjZ+V8bQn82GCRMmpGWXXbbZ6OIRIECAQD8Cs/Wz3eZR\nFIhKoRVWWCG98MILaZtttskri4rTR8+kvffeO1+NOYpWWWWVYlf+GRVLsT3+nXLKKTX7rBAg\nQIAAAQIExkpA+WWsZJ2XAIFuFthiiy3yRnzN3uOcc86ZjBTRrJZ4BAYXUH4Z3KhTY8SUD/PM\nM0/TyZ80aVL6j//4j6bji0iAAAECjQX0QGrsMqpbYw6k//qv/8p7IcX4q9EqbZNNNkmPP/54\n+vOf/5xmzpyZVl111XTSSSf1uW60rvjFL36Rb19kkUX67LeBAAECBAgQIDAWAsovY6HqnAQI\ndLvAtttumxZddNF8/ttKpTLg7Ubl0Wc/+9l8SKYBI9pJgEDTAsovTVN1XMTI2+hhdswxx6Ri\nXvD+biJ6Hy244IJp++237y+K7QQIECDQpIAeSE1CjTTadtttl/7whz+ktddeOz3zzDPpoosu\nSjFP0axZs9Luu++efve736WFFlpopJdxPAECBAgQIEBg1ASUX0aN0okIEOgRgZif49xzz82H\nsRvolqNl/EorrZS+/OUvDxTNPgIEhiGg/DIMtA455Itf/GI+ck/8Dh0oxHxY8bsFqbeGAABA\nAElEQVQ4KuoFAgQIEBiZwISsVdTAzaJGdn5HNxB4+umn0y233JLigRc9jxZeeOEGscZn08c+\n9rF0xhlnpDvuuCNP2/ikwlUJECBAgACBdhNQfmm3HJEeAgTaWeCqq65K73//+/NW8vUt5aOS\nab311ksxF65RJto5F6WtGwSUX7ohF2vv4cknn0w77LBD3kj7tddeS+XXmlFhFO/azjvvvLTV\nVlvVHmiNAAECBIYlYAi7YbGN7KAFFlggbbbZZiM7iaMJECBAgAABAi0UUH5pIbZLESDQ8QIx\nF9IDDzyQfvjDH6ZTTz01PfbYY/lQdWuttVY64IADDKvU8TnsBjpFQPmlU3Kq+XTG6D3XXntt\n+vWvf51OOOGENHXq1PTqq6/mw4futdde+Tzjke8CAQIECIyOgAqk0XF0FgIECBAgQIAAAQIE\nCBAgUBWYf/7508EHH5zWXHPNFK3kIyy//PLpzW9+czWOBQIECBAYnsB73/vetMIKK6R77703\nP0HMexTbBAIECBAYXQFzII2up7MRIECAAAECBAgQIECAAAECBAgQIECAAAECBDpeQAVSx2eh\nGyBAgAABAgQIECBAgAABAgQIECBAgAABAgQIjK6ACqTR9XQ2AgQIECBAgAABAgQIECBAgAAB\nAgQIECBAgEDHC6hA6vgsdAMECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAgdEVUIE0up7ORoAA\nAQIECBAgQIAAAQIECBAgQIAAAQIECBDoeAEVSB2fhW6AAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQIDC6AiqQRtfT2QgQIECAAAECBAgQIECAAAECBAgQIECAAAECHS+gAqnjs9ANECBAgAAB\nAgQIECBAgAABAgQIECBAgAABAgRGV0AF0uh6OhsBAgQIECBAgAABAgQIECBAgAABAgQIECBA\noOMFVCB1fBa6AQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIDA6AqoQBpdT2cjQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQIECHS8gAqkjs9CN0CAAAECBAgQIECAAAECBAgQIECAAAECBAgQGF0B\nFUij6+lsBAgQIECAAAECBAgQIECAAAECBAgQIECAAIGOF1CB1PFZ6AYIECBAgAABAgQIECBA\ngAABAgQIECBAgAABAqMroAJpdD2djQABAgQIECBAgAABAgQIECBAgAABAgQIECDQ8QIqkDo+\nC90AAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQGB0BVQgja6nsxEgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAAQIEOl5ABVLHZ6EbIECAAAECBAgQIECAAAECBAgQIECAAAECBAiMroAKpNH1dDYC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAQMcLqEDq+Cx0AwQIECBAgAABAgQIECBAgAABAgQI\nECBAgACB0RVQgTS6ns5GgAABAgQIECBAgAABAgQIECBAgAABAgQIEOh4ARVIHZ+FboAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBAgMLoCKpBG19PZCBAgQIAAAQIECBAgQIAAAQIECBAgQIAA\nAQIdL6ACqeOz0A0QIECAAAECBAgQIECAAAECBAgQIECAAAECBEZXQAXS6Ho6GwECBAgQIECA\nAAECBAgQIECAAAECBAgQIECg4wVUIHV8FroBAgQIECBAgAABAgQIECBAgAABAgQIECBAgMDo\nCqhAGl1PZyNAgAABAgQIECBAgAABAgQIECBAgAABAgQIdLyACqSOz0I3QIAAAQIECBAgQIAA\nAQIECBAgQIAAAQIECBAYXQEVSKPr6WwECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAgY4XUIHU\n8VnoBggQIECAAAECBAgQIECAAAECBAgQIECAAAECoyugAml0PZ2NAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQINDxAiqQOj4L3QABAgQIECBAgAABAgQIECBAgAABAgQIECBAYHQFVCCNrqez\nESBAgAABAgQIECBAgAABAgQIECBAgAABAgQ6XkAFUsdnoRsgQIAAAQIECBAgQIAAAQIECBAg\nQIAAAQIECIyugAqk0fV0NgIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAxwuoQOr4LHQDBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAAIHRFVCBNLqezkaAAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQ6HgBFUgdn4VugAABAgQIECBAgAABAgQIECBAgAABAgQIECAwugIqkEbX09kIECBAgAAB\nAgQIECBAgAABAgQIECBAgAABAh0voAKp47PQDRAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nRldABdLoejobAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQKDjBVQgdXwWugECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAwOgKqEAaXU9nI0CAAAECBAgQIECAAAECBAgQIECAAAECBAh0vIAK\npI7PQjdAgAABAgQIECBAgAABAgQIECBAgAABAgQIEBhdARVIo+vpbAQIECBAgAABAgQIECBA\ngAABAgQIECBAgACBjhdQgdTxWegGCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQKjK6ACaXQ9\nnY0AAQIECBAgQIAAAQIECBAgQIAAAQIECBAg0PECKpA6PgvdAAECBAgQIECAAAECBAgQIECA\nAAECBAgQIEBgdAVUII2up7MRIECAAAECBAgQIECAAAECBAgQIECAAAECBDpeQAVSx2ehGyBA\ngAABAgQIECBAgAABAgQIECBAgAABAgQIjK6ACqTR9XQ2AgQIECBAgAABAgQIECBAgAABAgQI\nECBAgEDHC6hA6vgsdAMECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAgdEVUIE0up7ORoAAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBDoeAEVSB2fhW6AAAECBAgQIECAAAECBAgQIECAAAECBAgQ\nIDC6AhNH93TORoAAgc4RuPfee9P555+f7rjjjlSpVNJqq62Wtt9++7Tyyit3zk1IKQECBAgQ\nIECAAAECBAgQIECAAAECBMZAQAXSGKA6JQEC7S3w0ksvpc985jPp9NNPT3POOWeaMWNGnuC5\n5porHXTQQekjH/lIOumkk1KsCwQIECBAgAABAgQIECBAgAABAgQIEOhFARVIvZjr7plADwu8\n8soradNNN0233nprmjVrVrXyKEiKiqRzzjknTZ06Nd1www1p8uTJPazl1gkQIECAAAECBAgQ\nIECAAAECBAgQ6FUBcyD1as67bwI9KnDooYfmlUcvv/xyvwKxb9q0aenggw/uN44dBAgQIECA\nAAECBAgQIECAAAECBAgQ6GYBFUjdnLvujQCBGoGnn346nXDCCWmgyqPigIhz4oknpn/+85/F\nJp8ECBAgQIAAAQIECBAgQIAAAQIECBDoGQEVSD2T1W6UAIHf/va3aeLE5kfunGOOOdLll18O\njgABAgQIECBAgAABAgQIECBAgAABAj0noAKp57LcDRPoXYG///3vQ7r5SqWS7r333iEdIzIB\nAgQIECBAgAABAgQIECBAgAABAgS6QUAFUjfkonsgQKApgUmTJqUJEyY0FTciRdw4RiBAgAAB\nAgQIECBAgAABAgQIECBAgECvCahAGoccj14NDz74YJoxY8aoX/3JJ59MTzzxxKif1wkJdIPA\nWmutlWbOnNn0rcyaNSvFMQIBAgQIpKT84ltAgAABAgQIdJqA8kun5Zj0EiBAgEC7CahAamGO\nxPBZH/zgB9M888yTll122TT//POnDTbYIB111FH5S5nhJuWZZ55Jn//859Niiy2WFl544bTo\nooumNdZYI33iE59I999//3BP6zgCXSew2Wabpfnmm6/p+5prrrnS5ptv3nR8EQkQINCNAsov\n3Zir7okAAQIECHS3gPJLd+evuyNAgACB1gk0P5t869LUlVe67bbb0sYbb5yisifCKquskh57\n7LF000035f9uv/32dPrpp6eJE4eWJY8++mhab7318h5NMdzWCiuskL8gv/POO1Oc85JLLkmX\nX365XhRd+a1yU0MVmGOOOdIJJ5yQ9txzz0F7IsXP4vHHH58mT5481MuIT4AAga4RUH7pmqx0\nIwQIECBAoGcElF96JqvdKAECBAi0QEAPpBYgv/LKK2nbbbfNK49iOKx777033XXXXflQc2ec\ncUZeaXTWWWelww47bMip2XnnnfPKo6WWWir9/ve/z889derUvOdR9Jx4+OGH0yabbJKee+65\nIZ/bAQS6UWD33XdPn/vc5wasrI3Ko/322y+vaOpGA/dEgACBZgSUX5pREocAAQIECBBoJwHl\nl3bKDWkhQIAAgW4QUIHUglw888wz8wqd2WabLV166aV5L6G47Oyzz5722GOPvJdDrJ988slD\nmhcpei9df/31cWj68Y9/nDbaaKN8Of5bYokl0pQpU/Lh8p5++ul01VVXVfdZINDrAsccc0w6\n99xz03LLLZei596kSZPyf7G8zDLLpJ/+9KfpO9/5Tq8zuX8CBHpcQPmlx78Abp8AAQIECHSg\ngPJLB2aaJBMgQIBAWwuoQGpB9kQvowhbbLFF/nI6Xyn9Fz0i4gX2U089lc4555zSnoEXb7zx\nxjTnnHOmpZdeOm255ZZ9Ii+yyCLVoeuuuOKKPvttINDLAjvuuGNesRtDRx5wwAFp//33T6ec\nckqaPn16+sAHPtDLNO6dAAECuYDyiy8CAQIECBAg0GkCyi+dlmPSS4AAAQLtLqACaYxzKLpP\n/+Uvf8mvsuuuuza82gILLFCtALrwwgsbxmm0MV56v/DCC+lPf/pTo935toceeij/XHbZZfuN\nYweBXhZYeeWV09vf/va8B98b3/jGXqZw7wQIEKgKKL9UKSwQIECAAAECHSKg/NIhGSWZBAgQ\nINBRAiqQxji7pk2bll5++eX8KiuttFK/V1txxRXzfX/729/6jdNoRwyDt+SSSzbalQ/R9eCD\nD+b7Yg4mgQABAgQIECDQjIDySzNK4hAgQIAAAQLtJKD80k65IS0ECBAg0C0CE7vlRtr1Ph5/\n/PFq0mJIuf7CQgstlO8qKnz6izfY9vvuuy9deeWV6ZJLLkkXX3xxinmXvvnNb6Z/+7d/a3ho\n9FC6+uqrq/seeeSRNHGir0UVxAIBAgQIEOhBAeWXHsx0t0yAAAECBDpcQPmlwzNQ8gkQIECg\nLQXUFIxxtjz77LPVKyy88MLV5fqFogLppZdeSrNmzcorfurjDLb+5JNPpqInUxH3mGOOSQcd\ndFCx2ufzrrvuSkcccUTN9jnmmKNm3QoBAgQIECDQWwLKL72V3+6WAAECBAh0g4DySzfkonsg\nQIAAgXYTUIE0xjkScxQVYcEFFywW+3zOP//81W1RiTT33HNX15tdmD59elp11VXzIe3uvPPO\nFL2JDj744HTttdemn/3sZ6l8jeKca6yxRjruuOOK1XTyySene+65p7pugQABAgQIEOg9AeWX\n3stzd0yAAAECBDpdQPml03NQ+gkQIECgHQVUII1xrpR7HT3//PNp8uTJDa8Y+yJMmDCh3zgN\nDyxtXGedddIdd9xR3XLmmWemffbZJx/ObptttknXX399dV+xsPjii6f3vve9xWo6//zz02uv\nvVZdt0CAAAECBAj0noDyS+/luTsmQIAAAQKdLqD80uk5KP0ECBAg0I4Cs7VjoropTUsttVT1\ndmKIuf5CsW/eeecd1vB1jc67xx57pBjCLsINN9yQLr/88kbRbCNAgAABAgQI1Agov9RwWCFA\ngAABAgQ6QED5pQMySRIJECBAoOMEVCCNcZYNtQBTzIU0Wsnac889qxVSN95442id1nkIECBA\ngACBLhZQfunizHVrBAgQIECgSwWUX7o0Y90WAQIECIyrgAqkMeZfbLHF0uyzz55f5aGHHur3\nasW+GIau2fD444+nqBSaNm1av4fEXEqLLLJIvv+pp57qN54dBAgQIECAAIFCQPmlkPBJgAAB\nAgQIdIqA8kun5JR0EiBAgEAnCahAGuPcmm222dK6666bXyXmF2oUZsyYkS677LJ81wYbbNAo\nSsNtH/rQh9Lb3/72tP/++zfcHxuj0uixxx7L96+11lr9xrODAAECBAgQIFAIKL8UEj4JECBA\ngACBThFQfumUnJJOAgQIEOgkARVILcitAw88ML/KBRdckJ5//vk+V7zwwgvTc889lw81t9NO\nO/XZ39+GLbfcMt917bXXprvuuqthtBNOOKG6fcMNN6wuWyBAgAABAgQIDCSg/DKQjn0ECBAg\nQIBAOwoov7RjrkgTAQIECHSygAqkFuReVAqtsMIK6YUXXkjbbLNNXllUXPamm25Ke++9d766\n8847p1VWWaXYlX9GxVJsj3+nnHJKzb6PfOQjafHFF08zZ85Mu+yyS3rggQeq+yuVSvrBD36Q\njjzyyHzbfvvtl/RAqvJYIECAAAECBAYRUH4ZBMhuAgQIECBAoO0ElF/aLkskiAABAgQ6XGBi\nh6e/I5IfcyD913/9V9p1113Tddddl5Zbbrm0ySabpJjD6M9//nNeAbTqqqumk046qc/9vPLK\nK+kXv/hFvr2Yy6iIFJVH55xzTtpqq63SLbfcklZfffX8vG94wxvSzTffnO6555486sYbb5yO\nO+644jCfBAgQIECAAIFBBZRfBiUSgQABAgQIEGgzAeWXNssQySFAgACBjhfQA6lFWbjddtul\nP/zhD2nttddOzzzzTLrooovSH//4xzRr1qy0++67p9/97ndpoYUWGnJq3vnOd6a//vWv6V3v\neld68cUX0+WXX57OO++8vPJo4YUXTt///vdTDHE3efLkIZ/bAQQIECBAgEBvCyi/9Hb+u3sC\nBAgQINCJAsovnZhr0kyAAAEC7SqgB1ILc2adddZJt956a3r66afzHkOTJk1K0fMoKnr6C7Ev\nhqMbKMQ5rrjiivy8t99+e3r22WfTGmuskZZddtmBDrOPAAECBAgQIDCogPLLoEQiECBAgAAB\nAm0moPzSZhkiOQQIECDQsQIqkMYh6xZYYIG02WabjfqV47wbbrjhqJ/XCQkQIECAAAECyi++\nAwQIECBAgECnCSi/dFqOSS8BAgQItJuAIezaLUekhwABAgQIECBAgAABAgQIECBAgAABAgQI\nECAwzgIqkMY5A1yeAAECBAgQIECAAAECBAgQIECAAAECBAgQINBuAiqQ2i1HpIcAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBAgMM4CKpDGOQNcngABAgQIECBAgAABAgQIECBAgAABAgQIECDQ\nbgIqkNotR6SHAAECBAgQIECAAAECBAgQIECAAAECBAgQIDDOAiqQxjkDXJ4AAQIECBAgQIAA\nAQIECBAgQIAAAQIECBAg0G4CKpDaLUekhwABAgQIECBAgAABAgQIECBAgAABAgQIECAwzgIq\nkMY5A1yeAAECBAgQIECAAAECBAgQIECAAAECBAgQINBuAiqQ2i1HpIcAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgMM4CKpDGOQNcngABAgQIECBAgAABAgQIECBAgAABAgQIECDQbgIT2y1B\no5WeSqWSpk2blu677770+OOPp8ceeyzNPvvsaZFFFkmLLrpoWnvttdOyyy47WpdzHgIECBAg\nQIDAiAWUX0ZM6AQECBAgQIBAiwWUX1oM7nIECBAgQKCFAl1VgfTiiy+mc889N1122WXpmmuu\nySuOBrJccskl0wYbbJB22mmntMMOO6S55pproOj2ESBAgAABAgRGXUD5ZdRJnZAAAQIECBAY\nYwHllzEGdnoCBAgQINAmAl1RgRS9jE488cR02mmnpaeeeqpp2kceeSSdf/75+b83vOEN6QMf\n+ED6zGc+k/dOavokIhIgQIAAAQIEhiGg/DIMNIcQIECAAAEC4yqg/DKu/C5OgAABAgRaLtDR\ncyDNmDEjHXbYYWnVVVdN3/rWt4ZUeVQv/eyzz6ZTTz01veUtb0kf//jH06OPPlofxToBAgQI\nECBAYMQCyi8jJnQCAgQIEBhHgfhb+dBDD01rrrlmWmCBBdLSSy+dj+hx6aWXjmOqXHqsBZRf\nxlp47M5/xRVXpB133DH/WY2f2TXWWCMdcsgh6eGHHx67izozAQIECHSNQMf2QPrLX/6SDz0X\nrV/KIeY32myzzdLyyy+fz3EU8xwV/+abb74UFUVPP/10euihh9Ktt96apk6dmv74xz+mO++8\nMz/NrFmz8p5MU6ZMSSeddFLafffdy6e3TIAAAQIECBAYtoDyy7DpHEiAAAECbSAQQ8Z/9KMf\nzVPy8ssv55/PPPNMuvDCC9PFF1+cNt9883TeeeelGOFD6B4B5ZfOzMvnn38+7brrrunyyy9P\n8a4r/kWIn9m///3v6fjjj8/ff334wx/uzBuUagIECBBoiUDHViD993//dyoqj5ZYYokUD7zt\nt98+bbjhhmm22frvWDX33HOniL/aaqulLbbYoop87733pmgxFRVH1113XYoH7bXXXqsCqSpk\ngQABAgQIEBipgPLLSAUdT4AAAQLjJfCrX/0q/7v7tdde65OESqWSZs6cmc9FvPXWW+d/U0+c\n2LGvG/rcX69vUH7pvG9A/Jy+5z3vSZF38bNZH4oK4KgQnmOOOdIuu+xSH8U6AQIECBDIBfqv\naekAoE033TSv8HnggQfScccdlzbaaKMBK48GuqUVV1wx7bPPPnml0d/+9rf0yU9+Mk2ePHmg\nQ+wjQIAAAQIECAxZQPllyGQOIECAAIFxFogeC/GiuVHlUTlpr7zySrr55pvzOYrL2y13voDy\nS2fl4cknn5xXHhUVRf2lPn6m99xzz/Tkk0/2F8V2AgQIEOhxgY5tEhTzFO29995jkn2rr756\n+tGPflTt3jsmF3FSAgQIECBAoOcElF96LsvdMAECBLpC4Oyzz06vvvpqU/cSL6yPPvrotP/+\n+zcVX6T2F1B+af88qk/hUUcdlQarPCqOiaHtzjzzzHTggQcWm3wSIECAAIGqQMf2QIoutmMd\nBhoKb6yv7fwECBAgQIBA9wkov3RfnrojAgQI9ILAZZddll566aWmb/XRRx9N999/f9PxRWxv\nAeWX9s6f+tQ9/PDDafr06fWb+12Pn+2Y0kEgQIAAAQKNBDq2AqnRzcS23XbbLZ8HKeZCuv32\n2/uLZjsBAgQIECBAoG0ElF/aJiskhAABAgQaCDz00EMNtva/afbZZ09RiSR0t4DyS3vm7z/+\n8Y80YcKEISUuKp0EAgQIECDQSKBjh7BrdDOxberUqem2227Ld7/wwgv9RbOdAAECBAgQINA2\nAsovbZMVEkKAAAECDQQWWWSRBlv73xTzqiy00EL9R7CnKwSUX9ozGxdccMFUqVSGlLih/owP\n6eQiEyBAgEBHC3RdD6SOzg2JJ0CAAAECBAgQIECAAAECbSaw+eabp8mTJzedqvnnnz+tvPLK\nTccXkQCB0RNYfvnl08ILL9z0Ceecc860xRZbNB1fRAIECBDoLYGu64FUzr7HHnssNdvVfuml\nly4fapkAAQIECBAgMC4Cyi/jwu6iBAgQIDCAwO67756+8pWvDBDj9V3xMnqfffZJ5hR+3aQX\nlpRf2ieXY/i6fffdNx1zzDHp5ZdfHjRh0WNwjz32GDSeCAQIECDQmwJdXYG0zTbbNJ2rQ+3e\n2/SJRSRAgAABAgQIDEFA+WUIWKISIECAQEsEosHl0Ucfnb74xS+mV199td9rTpw4MS255JLp\nkEMO6TeOHd0poPzSXvl60EEHpZ/97GfpvvvuSzNnzuw3cXPMMUf6+te/npZbbrl+49hBgAAB\nAr0tYAi73s5/d0+AAAECBAgQIECAAAECBAYV+NznPpdXDEXPoka9i6Ln0YorrpiuueaaNN98\n8w16PhEIEBg7gXnmmSddffXV+VCS8bNZH4qf489//vN5xXD9fusECBAgQKAQUIFUSPgkQIAA\nAQIECBAgQIAAAQIE+hX42te+lm688ca09dZbp+i5UITovXDkkUemv/71rynmXxEIEBh/gWWW\nWSZNnTo1H8qu/HMZPQW33HLLdP311+c/t+OfUikgQIAAgXYW6Ooh7Hbbbbe0+OKLt7O/tBEg\nQIAAAQIEagSUX2o4rBAg0GMCs2bNSjF/R/wT2lNg/fXXTxdccEG65JJL0vPPP58mT56c1lxz\nzbTaaqu1Z4KlqiUCyi8tYR7yRSZNmpT233//vNL3tttuSy+99FKad95507vf/e4U+4T2FYip\nNuJfox6f7ZtqKSNAoBsFuroC6YADDkjrrrtuN+abeyJAgAABAgS6VED5pUsz1m0RINCvwKOP\nPpqOPfbYNGXKlPTII4/kL8tiKLSPfvSj+YvPeNkptKeAvGnPfBmPVCm/jIf60K4ZPY/8zA7N\nrNWxX3jhhfT9738/nX766emee+5J0ahiiSWWSDvvvHM6+OCD01JLLdXqJLkeAQIEkiHsfAkI\nECBAgAABAgQIECBAYFwEfvOb36SVVlopnXTSSenhhx/OW1u/9tpr6e67705HHHFEeuMb35hu\nueWWcUmbixIgQIAAgVYJxBCgq6yySjr88MPTXXfdleJZGD2QomHFD3/4w/xZeeGFF7YqOa5D\ngACBqoAKpCqFBQIECBAgQIAAAQIECBBolcANN9yQ3ve+96UZM2akl19+uc9lY9vjjz+eNt10\n03T//ff32W8DAQIECBDoBoEHH3wwveMd70j/+Mc/Gj4PX3nllXz7jjvumK699tpuuGX3QIBA\nBwmoQOqgzJJUAgQIECBAgAABAgQIdINAtKzefffd8xbWA91PDN/z4osvpn333XegaPYRIECA\nAIGOFfjsZz+bYvi6eOYNFIpn58yZMweKZh8BAgRGVaCr50DaZJNN0uyzz94UWEz+KRAgQIAA\nAQIExltA+WW8c8D1CRBohcA111yTpk+f3tSl4kVZDHUXw/gsueSSTR0jEgECrRVQfmmtt6t1\nj0D0tL3gggvy4eqauauYN/DKK69MW2+9dTPRxSFAgMCIBbq6Aumll14aMZATECBAgAABAgRa\nKaD80kpt1yJAYLwErr/++ryxX7OtqCdPnpxiyLuddtppvJLsugQIDCCg/DIAjl0EBhD4wx/+\nkOacc87U7M/QhAkT0u9//3sVSAOY2kWAwOgKGMJudD2djQABAgQIECBAgAABAgQGEfjnP/+Z\nYk6HZsNss82WnnjiiWaji0eAAAECBDpCIJ5t8YxrNsSzM56hAgECBFol0NU9kDbeeOO0wAIL\ntMrSdQgQIECAAAECIxZQfhkxoRMQINABAosuumiaNGlSw8nCGyU/5oWIYwQCBNpTQPmlPfNF\nqtpfIJ5tMbdRsyGenYsttliz0cUjQIDAiAW6ugLpO9/5Tlp33XVHjOQEBAgQIECAAIFWCSi/\ntEradQgQGE+BTTfdNB1xxBFNJ+Hll19O8YJaIECgPQWUX9ozX6Sq/QU22mijIfXIrVQqKZ6h\nAgECBFol0NUVSK1CdB0CvSBw5513pmnTpqVXX301rbTSSumtb33rkLpZ94JRu9xjFChvvvnm\ndPfdd6c55pgjrb766vm/dkmfdBAgQIAAAQIENtlkk7Tyyiunu+66a9CJw6M8s91222lx7WtD\ngAABAl0nsNBCC6Vddtkl/epXvxq0IinmP1p22WXTO9/5zq5zcEMECLSvQPODbLbvPUgZAQJj\nKHDllVem1VZbLf/34Q9/OO25555pww03TIsvvng65ZRTxvDKTj0cgdNPPz3Pm/XXXz/Pq8iz\nNddcM73pTW9Kl19++XBO6RgCBAgQIECAwKgLxHwPZ599dpo4ceA2jbPPPnuab7750ve+971R\nT4MTEiBAgACBdhA44YQT0vzzz5/imTdQiP0//elPB4030DnsI0CAwFAFBi6tD/VsbRD/G9/4\nRnr66afzlKy44optkCJJINC5AjEMwRe+8IXqeLwzZsyo3kxM2rjffvulq6++Oi/AREsYYfwE\notfRHnvskc4999y8l1ik5MUXX6wmKHojbbPNNunII49MBx10UHW7BQIE2kNA+aU98kEqCBBo\nrUAMN37ZZZel7bffPm91HcPUlcOcc86Z9zq64oor0lJLLVXeZZkAgTYQUH5pg0yQhK4QiAa6\n119/fdpqq63SI4880md+wHgeRoOL888/P22wwQZdcc9uggCBzhHougqk973vfZ2jL6UE2lgg\n/lAvVx41Suorr7ySfvnLX+bDo335y19uFMW2Fgkce+yxacqUKdXKo/rLRgVTTMz5pS99Ke+R\nFJVJAgEC7SOg/NI+eSElBAi0VmDzzTdP999/f4rW16eddlp67LHH8mGSl19++bTvvvumT33q\nUylenAkECLSfgPJL++WJFHWuQIwaElMHxEgv3//+99O9996bZs2alRZddNF8dJEDDjggLbzw\nwp17g1JOgEDHCnRdBVLH5oSEE2gzgfiDPQorg4WoRIqWZ3vvvXdaZJFFBotu/xgIPPXUU+mr\nX/3qoOMlx6WjEinyVgXSGGSEUxIgQIAAAQLDElhwwQXT1772tbTxxhtXe1AvscQS6W1ve9uw\nzucgAgQIECDQiQKTJk3K/15fb7318p5IcQ+TJ0/OeyZ14v1IMwEC3SFgDqTuyEd3QWBUBW67\n7bZ0zz33DDqhcXHRGMP+wgsvLFZ9tljg4osvHtIVp0+fnm6++eYhHSMyAQIECBAgQIAAAQIE\nCBAgQIAAAQK9JaACqbfy290SaEogKpDmmmuupuJGpFdffTVNmzat6fgijq5A5NfMmTObPmm0\nYIpjBAIECBAgQIAAAQIECBAgQIAAAQIECPwfe3cCJldVJgz4y55JgIQkIEICCYtRloAsThzZ\nZBcSBIGfMBoBl2EQfgSMwyLIAP4qqDjgjDKICAKyCoQoiwqIiJIRkJ1hDxggECAGAllJ/pzL\nU2Wnu6u7q7uq61bVe58n9K17zj3n3PdUN1/3V+feUgISSKVkHCfQxAKtH2DcGUW61d2iRYs6\nq6a8SgLpNoJdud1gy+7TOTYCBAgQIECAAAECBAgQIECAAAECBAiUEpBAKiXjOIEmFthwww27\n9DydAlFa0bLRRhsVXvraywLjxo0r6+HSacVYmmMbAQIECBAgQIAAAQIECBAgQIAAAQIESglI\nIJWScZxAEwt89KMfjSFDhnRZIK0+mjRpUpfrq1hZgWRfzgqw9GDO9JBqGwECBAgQIECAAAEC\nBAgQIECAAAECBEoJSCCVknGcQBML9O/fP04//fRIiYbOtlTnU5/6VIwfP76zqsqrJJBWE02Z\nMqVLq5DSfJ166qldmtsqDVezBAgQIECAAAECBAgQIECAAAECBAjUgYAEUh1MkiESqIXAMccc\nE7vvvnuHSYmUjBg9enRceOGFtRiiPlsInH/++bH++ut3mBgaNGhQ7LzzzvHVr361xZl2CRAg\nQIAAAQIECBAgQIAAAQIECBAg0Fagf9tD9XHktddeixdeeKGqgx01alT2B9mqdqJxAjkV6Nu3\nb0yfPj1OPvnkOOecc6Jfv36xePHibLQpcZSeo7P33nvHT3/60xg+fHhOr6J5hrXGGmvEn//8\n5/j85z8f1113XQwYMKD4HKuUOFq2bFkcddRRcdZZZ0WaWxsBArUREL/Uxl2vBAgQIECAQPcF\nxC/dt3MmAQIECBCod4G6TSBdc8018aUvfamq/ukPsVZWVJVY4zkXSEmjlHD48pe/HN///vfj\n4YcfzhIRY8aMiWnTpsVmm22W8ytoruENGzYsrr322nj88cfje9/7XsyaNStL/G2++eZx3HHH\nZavFmkvE1RLIn4D4JX9zYkQECBAgQIBAxwLil459lBIgQIAAgUYWqNsEUiNPimsjkDeBdddd\nNw466KDYfvvts6ENHjxY8ihvk9RiPB/60Ifi4IMPjnfeeSc7us4660getfCxS4AAAQIECBAg\nQIAAAQIECBAgQIBA5wJ1m0BKz/pIt8+q5jZhwoRqNq9tAgQIECBAoMkExC9NNuEulwABAgQI\nNICA+KUBJtElECBAgACBbgrUbQJpn332ifTPRoAAAQIECBCoFwHxS73MlHESIECAAAECBQHx\nS0HCVwIECBAg0HwCnqTefHPuigkQIECAAAECBAgQIECAAAECBAgQIECAAAECHQpIIHXIo5AA\nAQIECBAgQIAAAQIECBAgQIAAAQIECBAg0HwCEkjNN+eumAABAgQIECBAgAABAgQIECBAgAAB\nAgQIECDQoYAEUoc8CgkQIECAAAECBAgQIECAAAECBAgQIECAAAECzScggdR8c+6KCRAgQIAA\nAQIECBAgQIAAAQIECBAgQIAAAQIdCkggdcijkAABAgQIECBAgAABAgQIECBAgAABAgQIECDQ\nfAISSM03566YAAECBAgQIECAAAECBAgQIECAAAECBAgQINChgARShzwKCRAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQLNJ9BwCaR777033n333eabSVdMgAABAgQI1K2A+KVup87ACRAgQIBA\n0wqIX5p26l04AQIECDSRQMMlkA4//PAYM2ZMTJs2LR566KFcTuWKFSti9uzZsXDhwoqPL7U5\na9asWLp0acXb1iABAgQIECBQHQHxi/ilOu8srRIgQIAAgeoJiF/EL9V7d2mZAAECBPIi0HAJ\npAT78ssvx/e+973YcsstY6uttopzzjkn5syZU3PzZ599Ng455JAYOnRoluQaNmxYTJw4Mb71\nrW9FSip1d3vzzTfjxBNPjPXXXz9re9y4cTFkyJD44Ac/GD/4wQ+syOourPMIECBAgEAvCohf\nxC+9+HbTFQECBAgQqIiA+EX8UpE3kkYIECBAILcCDZlAaqn94IMPxle+8pUYPXp07L333nHl\nlVdWZeVPyz7b23/kkUdi6623Lva/ySabZEmemTNnxsknnxyHHnpoLFu2rL1TOzyWklIf+MAH\n4qyzzoq//vWvMWLEiJgwYUIMHjw4nnjiiTjmmGPiox/9aLz99tsdtqOQAAECBAgQyI+A+EX8\nkp93o5EQIECAAIGuCYhfxC9de6eoRYAAAQL1JNBwCaQvfvGLsfnmm7eZg/RcpJtvvjlbAbTO\nOuvEF77whfj973/fo5U/bTopcWDJkiUxadKkmD9/fja25557Lp588sl4/fXX4+KLL47+/fvH\npZdeGqecckqJFto/nG5Tl1Y0vfLKK1mC7Ne//nW89tprkYK21FdafTRw4MD485//HMcdd1z7\njThKgAABAgQI1FxA/CJ+qfmb0AAIECBAgECZAuIX8UuZbxnVCRAgQKAOBRougZRW3Dz88MPx\nv//7v/GNb3wju4Vd63lJt3z7yU9+EjvttFNsuOGG8fWvfz1L6LSuV6nXl1xySTz//PPRt2/f\nLIk1duzYrOl+/fplK4/SLfbSdsEFF5S1Ouo3v/lN/M///E/06dMnLr/88th9992zdtJ/Ul9H\nH310nHbaadmxH//4xzF37txiuR0CBAgQIEAgPwLil/fmQvySn/ekkRAgQIAAgc4ExC/vCYlf\nOnunKCdAgACBehZouARSYTLGjx8fX/va1+Ivf/lLPPXUU9lzhrbZZptCcfHrrFmz4swzz4xU\n/x//8R/jqquuiuXLlxfLK7GTVhmlbdddd81WCmUvWvxn6tSp2UqhefPmxRVXXNGipOPdO++8\nM6uQxr7jjju2W/nTn/508XiysBEgQIAAAQL5FRC/vDc34pf8vkeNjAABAgQItBYQv7wnIn5p\n/c7wmgABAgQaQaBhE0gtJ2fjjTeOE088Me6999545pln4oADDmhZXNxPq3mmTJkSH/7wh7Pn\nCRULerCTbl933333ZS2kttvbhg8fHnvssUdWNH369PaqtHtsl112yVZZHXvsse2Wp4ODBg0q\nlnkOUpHCDgECBAgQyL2A+OW9KRK/5P6taoAECBAgQKAoIH55j0L8UnxL2CFAgACBOhfoX+fj\n7/Lw03OArr766rjmmmuy28l1dOJDDz2UJXQeffTR7FZwHdXtrCy1sXjx4qxaul1eqW3cuHFZ\n0WOPPVaqSpvje+65Z6R/HW133HFHsXjbbbct7tshQIAAAQIE8i8gfokQv+T/fWqEBAgQIECg\npYD4RfzS8v1gnwABAgTqW6ChE0j3339/ljRKiaPnnnuu5EztsMMOkVYKzZw5s1gnPUPppptu\nikmTJhWPdWen5XOHRo0aVbKJESNGZGWzZ88uWafcgnRN6flOaZswYUKMGTOm3CbUJ0CAAAEC\nBHpZQPwifunlt5zuCBAgQIBAjwXEL+KXHr+JNECAAAECuRRouATSww8/HFdeeWWWOHr66adL\noo8ePTo++9nPxuGHHx5piXXabr311th3332zZFJ6nZ4Z1NME0ptvvpmayraRI0cWdtt8LSSQ\nFi1alD2DKT2EsSfbihUrsmtLBv3794+LLrqo3eaeeOKJuOyyy4pl6RZ/AwYMKL62Q4AAAQIE\nCFRfQPzynrH4pfrvNT0QIECAAIFKCYhf3pMUv1TqHaUdAgQIEMijQMMlkP75n/85HnnkkXat\n0/OA9ttvvyyxsvvuu7e5PV26HdynPvWpLAGVGpgzZ0677ZRzsOV9b9dcc82Spw4bNqxYlpJI\nQ4YMKb4udycFL1/+8pfj5z//eXbqySefHNtss027zbz00ktZsq1lYUo42QgQIECAAIHeExC/\nRIhfeu/9picCBAgQIFAJAfGL+KUS7yNtECBAgEC+BZoiU5DunZ9WGh1yyCHRURInTdXkyZOL\nCaSOVgx1dVpbtrFgwYIYPHhwu6emsrT16dOnZJ12T2x1MN227nOf+1xcfvnlWcmRRx4Z//7v\n/96q1t9fbrfddnHjjTcWD5x66qnx1FNPFV/bIUCAAAECBGojIH7595Lw4peSNAoIECBAgEBN\nBcQv/17SX/xSkkYBAQIECORYoGETSGuvvXZ8+tOfzhJHW2yxRZenYPHixZHqp+cF7bTTTl0+\nr1TFddddt1j0xhtvRKnnIKWytK222mptVkYVG+hkZ/78+bH//vvHHXfckdWcNm1anH322VlS\nqtSpqb/x48cXi4cOHZp9Arh4wA4BAgQIECDQawLilwjxS6+93XREgAABAgQqIiB+Eb9U5I2k\nEQIECBDIpUDDJZD22muvOPPMM2Offfbp1rN80kql9K9SW+sEUql2CwmkwrOQStUrdfyFF16I\nvffeOx599NEsAXXuuefG0UcfXaq64wQIECBAgECOBMQv4pccvR0NhQABAgQIdElA/CJ+6dIb\nRSUCBAgQqGuBhksgfec738nVhKRP4vTr1y/efffdePHFF0uOrVC25ZZblqxTqiAljdIznV5+\n+eVIK4jS7es++clPlqruOAECBAgQIJAzAfGL+CVnb0nDIUCAAAECnQqIX8Qvnb5JVCBAgACB\nuhfoW69XcNFFF8VnPvOZuPvuuyt+Ca+99lq2iumUU07pcdt9+/aNdA/gtF1//fXttrdw4cK4\n5ZZbsrKJEye2W6fUwaeffjp22223LHn0vve9L+68807Jo1JYjhMgQIAAgRoLiF/emwDxS43f\niLonQIAAAQJlCIhf3sMSv5TxplGVAAECBBpGoG4TSOlZRWmlzfbbbx9p1U66ZdusWbO6PTHp\n+UE33nhjHHLIITF69Oj4+te/HnPmzOl2ey1PPO6447KXN9xwQyxYsKBlUbY/ffr0eOutt7Jb\nzx144IFtyksdWLFiRXz2s5/NxpmerfT73/8+ttlmm1LVHSdAgAABAgRqLCB+iexZi+KXGr8R\ndU+AAAECBMoQEL+IX8p4u6hKgAABAg0mULe3sNtss80i3R7u1VdfjYceeiiOPfbY7F9KJu26\n664xduzYGDNmTPFfqpu2pUuXZue88sorMXv27GwF0x133BH3339/dpu5wvym285NmDCh8LJH\nX1NSKI0nJbjSs5l++ctfxuqrr561OXPmzDjyyCOz/YMOOig22WSTVfpKiaXPfe5z2bE99tgj\nvvjFLxbL06eA/vSnP2WvjzjiiHjppZeyf8UKrXZS2+utt16ro14SIECAAAECvSUgfokQv/TW\nu00/BAgQIECgMgLiF/FLZd5JWiFAgACBehSo2wTSjjvuGM8880x8//vfj+9+97vx5ptvZv4P\nPvhgpH+tt8GDB8eQIUNi3rx52SdfW5e3fL3LLrtk7VYqgZSSUeedd15MmTIlWyW0/vrrxw47\n7BBz586Ne++9N5YtWxbjx4+PH/7why2Hke0vWbIkrr322mw/rTJquX3ta18rvvx//+//RfrX\n0faDH/wgjj766I6qKCNAgAABAgSqKCB+iRC/VPENpmkCBAgQIFAFAfGL+KUKbytNEiBAgECd\nCNTtLeyS72qrrRannnpqPPvsszFt2rRISaJS26JFi+KNN94omTxKzypKq4NuuummuO222yq2\n+qgwnsmTJ8cf//jHrN10u7wZM2bEPffcE8uXL4+pU6fG7bffHiNGjChU7/Triy++GGkVlY0A\nAQIECBCoLwHxi/ilvt6xRkuAAAECBPz9xd9ffBcQIECAQLMK1O0KpJYTNnLkyPjOd76T3cLu\nsssui1tuuSW7NV26XV1H24ABA2LbbbeNPffcMw4//PBIK4OquaXb66XVUX/729/igQceiIED\nB2Yrj9L4S22pLD3rqPWWbkXX3vHW9bwmQIAAAQIE8ikgfsnnvBgVAQIECBAgUFpA/FLaRgkB\nAgQIEGhEgYZIIBUmJiVVTjjhhOzfggULshU/aaVOek5S+rRIulVcehbSWmutFRtvvHF89KMf\nzW5rVzi/t74OHz48dt55597qTj8ECBAgQIBAjgXELzmeHEMjQIAAAQIE2hUQv7TL4iABAgQI\nEGg4gbpNIKXVN8cdd1ykVT077bRTbLjhhqtMTro9zB577LHKMS8IECBAgAABArUUEL/UUl/f\nBAgQIECAQHcExC/dUXMOAQIECBBoDIG6fQbSCy+8EOeee2587nOfiwsvvLA4G1/4whdit912\ny/4tXLiweNwOAQIECBAgQKDWAuKXWs+A/gkQIECAAIFyBcQv5YqpT4AAAQIEGkegblcgPfHE\nE8VZGDFiRHF/5syZ8cgjj2Sv33333eJxOwQIECBAgACBWguIX2o9A/onQIAAAQIEyhUQv5Qr\npj4BAgQIEGgcgbpdgZSea1TYrrvuunj00UcjLatO/wpby/3CMV8JECBAgAABArUSEL/USl6/\nBAgQIECAQHcFxC/dlXMeAQIECBCof4G6XYGUnn1U2P70pz/F5ptvXnhZ/LrGGmsU9zvbkWzq\nTEg5AQIECBAg0FMB8UtPBZ1PgAABAgQI9LaA+KW3xfVHgAABAgTyI1C3K5A222yzWH311fMj\naSQECBAgQIAAgU4ExC+dACkmQIAAAQIEcicgfsndlBgQAQIECBDoNYG6TSD17ds3Lr/88hg4\ncGCvYemIAAECBAgQINATAfFLT/ScS4AAAQIECNRCQPxSC3V9EiBAgACBfAjU7S3sEt/kyZPj\n7rvvjuuvvz5efvnlWLhwYdx8880xf/78TPeAAw6I/v3r+hLz8S4xCgIECBAgQKBiAuKXilFq\niAABAgQIEOglAfFLL0HrhgABAgQI5Eyg7rMr2267baR/hW2LLbYoJpAuvvjiWG211QpFvhIg\nQIAAAQIEciEgfsnFNBgEAQIECBAgUIaA+KUMLFUJECBAgECDCNR9Aqn1POyyyy6x8cYbZ4et\nPmqt4zUBAgQIECCQRwHxSx5nxZgIECBAgACBjgTELx3pKCNAgAABAo0h0HAJpHPPPbcxZsZV\nECBAgAABAk0jIH5pmql2oQQIECBAoGEExC8NM5UuhAABAgQIlBToW7JEAQECBAgQIECAAAEC\nBAgQIECAAAECBAgQIECAQFMKSCA15bS7aAIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAaQEJ\npNI2SggQIECAAAECBAgQIECAAAECBAgQIECAAAECTSkggdSU0+6iCRAgQIAAAQIECBAgQIAA\nAQIECBAgQIAAAQKlBSSQStsoIUCAAAECBAgQIECAAAECBAgQIECAAAECBAg0pYAEUlNOu4sm\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECJQWkEAqbaOEAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQINCUAhJITTntLpoAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgUFpAAqm0jRICBAgQIECA\nAAECBAgQIECAAAECBAgQIECAQFMKSCA15bS7aAIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBA\naQEJpNI2SggQIECAAAECBAgQIECAAAECBAgQIECAAAECTSkggdSU0+6iCRAgQIAAAQIECBAg\nQIAAAQIECBAgQIAAAQKlBSSQStsoIUCAAAECBAgQIECAAAECBAgQIECAAAECBAg0pYAEUlNO\nu4smQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECJQWkEAqbaOEAAECBAgQIECAAAECBAgQIECA\nAAECBAgQINCUAhJITTntLpoAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgUFpAAqm0jRICBAgQ\nIECAAAECBAgQIECAAAECBAgQIECAQFMKSCA15bS7aAIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQIBAaQEJpNI2SggQIECAAAECBAgQIECAAAECBAgQIECAAAECTSkggdSU0+6iCRAgQIAAAQIE\nCBAgQIAAAQIECBAgQIAAAQKlBSSQStsoIUCAAAECBAgQIECAAAECBAgQIECAAAECBAg0pYAE\nUlNOu4smQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECJQWkEAqbaOEAAECBAgQIECAAAECBAgQ\nIECAAAECBAgQINCUAhJITTntLpoAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgUFpAAqm0jRIC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAQFMKSCA15bS7aAIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIBAaQEJpNI2SggQIECAAAECBAgQIECAAAECBAgQIECAAAECTSkggdSU0+6iCRAgQIAA\nAQIECBAgQIAAAQIECBAgQIAAAQKlBSSQStsoIUCAAAECBAgQIECAAAECBAgQIECAAAECBAg0\npYAEUlNOu4smQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECJQWkEAqbaOEAAECBAgQIECAAAEC\nBAgQIECAAAECBAgQINCUAhJITTntLpoAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgUFpAAqm0\njRICBAgQIECAAAECBAgQIECAAAECBAgQIECAQFMKSCA15bS7aAIECBAgQIAAAQIECBAgQIAA\nAQIECBAgQIBAaQEJpNI2SggQIECAAAECBAgQIECAAAECBAgQIECAAAECTSkggdSU0+6iCRAg\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQKlBSSQStsoIUCAAAECBAgQIECAAAECBAgQIECAAAEC\nBAg0pYAEUlNOu4smQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECJQWkEAqbaOEAAECBAgQIECA\nAAECBAgQIECAAAECBAgQINCUAhJITTntLpoAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgUFpA\nAqm0jRICBAgQIECAAAECBAgQIECAAAECBAgQIECAQFMKSCA15bS7aAIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQIBAaQEJpNI2SggQIECAAAECBAgQIECAAAECBAgQIECAAAECTSkggdSU0+6i\nCRAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQKl+kG9UAAAQABJREFUBSSQStsoIUCAAAECBAgQ\nIECAAAECBAgQIECAAAECBAg0pYAEUlNOu4smQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECJQW\nkEAqbaOEAAECBAgQIECAAAECBAgQIECAAAECBAgQINCUAhJITTntLpoAAQIECBAgQIAAAQIE\nCBAgQIAAAQIECBAgUFpAAqm0jRICBAgQIECAAAECBAgQIECAAAECBAgQIECAQFMKSCA15bS7\naAIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAaQEJpNI2SggQIECAAAECBAgQIECAAAECBAgQ\nIECAAAECTSkggdSU0+6iCRAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQKlBSSQSttUrWTFihUx\ne/bsWLhwYdX6eOmll+KJJ56oWvsaJkCAAAECBJpLQPzSXPPtagkQIECAQCMIiF8aYRZdAwEC\nBAjUUkACqRf1n3322TjkkENi6NChMWbMmBg2bFhMnDgxvvWtb0UKaiq1vfrqqzFhwoSs7Uq1\nqR0CBAgQIECgOQXEL805766aAAECBAjUs4D4pZ5nz9gJECBAIE8C/fM0mEYeyyOPPBLbb799\nzJ8/P7vMTTbZJFKiZ+bMmdm/xx9/PC666KLo379nU/LOO+/EgQceGK+//noMHz68kUldGwEC\nBAgQIFBlAfFLlYE1T4AAAQIECFRcQPxScVINEiBAgEATC1iB1AuTv2TJkpg0aVKWPNp8883j\nueeeiyeffDJL8lx88cVZ0ujSSy+NU045pUejeeGFF2KvvfaKu+66q0ftOJkAAQIECBAgIH7x\nHiBAgAABAgTqTUD8Um8zZrwECBAgkHcBCaRemKFLLrkknn/++ejbt2/cfPPNMXbs2KzXfv36\nxaGHHhrnnHNO9vqCCy7o1nOR0u3vfvjDH0ZKTkke9cKE6oIAAQIECDSBgPilCSbZJRIgQIAA\ngQYTEL802IS6HAIECBCouYAEUi9MQVpllLZdd901Ro8ene23/M/UqVNj4MCBMW/evLjiiita\nFnW6n25Zt/POO8dRRx0Vb731VpZEOvroozs9TwUCBAgQIECAQEcC4peOdJQRIECAAAECeRQQ\nv+RxVoyJAAECBOpZQAKpyrOXlk/fd999WS9Tpkxpt7f0rKI99tgjK5s+fXq7dUodfPPNN+P3\nv/99DBgwII455pj485//HJtttlmp6o4TIECAAAECBDoVEL90SqQCAQIECBAgkDMB8UvOJsRw\nCBAgQKAhBPo3xFXk+CIeffTRWLx4cTbCDTfcsORIx40bl5U99thjJeu0V5Bug/cv//IvcdJJ\nJxVvjddePccIECBAgAABAl0VEL90VUo9AgQIECBAIC8C4pe8zIRxECBAgEAjCUggVXk2586d\nW+xh1KhRxf3WOyNGjMgOzZ49u3VRh6/XWmut+O///u8O6yjsfYFFixZlz7Nac801e79zPRJo\ncIF0u8/BgwfHP/zDPzT4lbo8ArUTEL/Uzl7PBAgQIECAQPcExC/dc3MWAQIECBDoSEACqSOd\nCpSlW8wVtpEjRxZ223wtJJBS4mH58uXRt2/v3F0w3V7vrLPOKo7nmWeeiUGDBhVf2+m6wIIF\nC+J73/te/OQnP4m//vWv2Ynpj9yf+MQn4rTTTostt9yy642pSYDAKgIPP/xwnH766XHTTTdl\nydlUuN5668XnP//5mDZtWqy++uqr1PeCAIGeCYhfeubnbAIECBAgQKD3BcQvvW+uRwIECBBo\nfAEJpCrP8dtvv13soaPVKMOGDSvWS0mkIUOGFF9XcycFWA8++OAqXfRW8mqVTuv8xeOPPx67\n7bZbvP7668VbFqZLSnM5Y8aMSM+2+s53vhPHH398nV+p4RPofYHzzjsvjjvuuCyxvmzZsuIA\nXnzxxSwBfsEFF8RvfvOb2HzzzYtldggQ6JmA+KVnfs4mQIAAAQIEel9A/NL75nokQIAAgcYX\n6J1lLo3vWPIKW646SitUSm2Fsj59+mS3ZipVr9LHP/7xj8cTTzxR/PdP//RPxU/3V7qvRm3v\n1VdfjZ122ileeeWVVZJHhetNf/BOq8pOOOGEuPjiiwuHfSVAoAsCl19+eXzlK1/JvodaJo8K\np6ZnzKXvwZ133jnmzJlTOOwrAQI9FBC/9BDQ6QQIECBAgECvC4hfep1chwQIECDQBAISSFWe\n5HXXXbfYwxtvvFHcb71TKFtttdV67fZ1rcfgdfcETjrppJg/f368++67HTaQ/vh99NFHR3p+\ni40Agc4F0grJI488MtpLHLU8OyVo33rrrfjqV7/a8rB9AgR6ICB+6QGeUwkQIECAAIGaCIhf\nasKuUwIECBBocAEJpCpPcLkBTOFZSFUeluYrJLBw4cK47LLLYsmSJV1qMSWZrrnmmi7VVYlA\nswtcd911sXTp0i4xpO/BK6+8MgqrObt0kkoECJQUEL+UpFFAgAABAgQI5FRA/JLTiTEsAgQI\nEKhrAQmkKk/f2muvHf369ct6Sc/rKLUVyrbccstSVRzPocADDzzQ6cqjlsNOz0S66667Wh6y\nT4BACYE//OEP2XPEShS3e/j+++9v97iDBAiUJyB+Kc9LbQIECBAgQKD2AuKX2s+BERAgQIBA\n4wlIIFV5Tvv27Rvbbrtt1sv111/fbm9pFcstt9ySlU2cOLHdOg7mUyDdjm7AgAFlDW7u3Lll\n1VeZQLMKpGcblbOl70W3iCxHTF0CpQXEL6VtlBAgQIAAAQL5FBC/5HNejIoAAQIE6ltAAqkX\n5u+4447Lernhhhvavb3S9OnTs+d3pGDnwAMP7IUR6aJSAuuss06Xb1+X+uzTp0+MGTOmUt1r\nh0BDC6TvlfRzsatbuo1d+p60ESBQGQHxS2UctUKAAAECBAj0noD4pfes9USAAAECzSHQ9b/M\nNYdHVa4yJYXGjh0bb7/9duyzzz5ZsqjQ0cyZM7OHxKfXBx10UGyyySaFouxrejB8Op7+/fjH\nP16lzIvaC6RbDg4ZMqTLAxk4cGDstttuXa6vIoFmFth1112jf//+XSZI319bb711l+urSIBA\nxwLil459lBIgQIAAAQL5ExC/5G9OjIgAAQIE6lug63+Zq+/rrOno0zOQzjvvvJgyZUr8/ve/\nj/XXXz922GGHSLcyu/fee2PZsmUxfvz4+OEPf9hmnOkT9ddee212fNSoUW3KHaitQJrb448/\nPs4666xYvHhxp4MZPnx47Lfffp3WU4EAgYjJkyfHWmutFYVnxHVkMmjQoDjmmGPKvqVkR20q\nI9DsAuKXZn8HuP68C6TfE9KWPkBhI0CAAIH3BMQv3gkE8i0gfsn3/BgdgfYErEBqT6UKx9If\nQv/4xz/GhAkTYv78+TFjxoy45557Yvny5TF16tS4/fbbY8SIEVXoWZPVFjjxxBNj44037vSX\n9xTIXnHFFZH+0G0jQKBzgfRMo/Q909kqpPSHs3HjxsWpp57aeaNqECBQloD4pSwulQlUXSB9\nAG3atGmx7rrrZjFliivT7VvTLZvKfXZg1QerAwIECNRIQPxSI3jdEighIH4pAeMwgToRsAKp\nFycq3e7swQcfjL/97W/xwAMPZAmHtPJo5MiRJUeRylasWFGyvL2Cf/3Xf430z9Y7Av/wD/8Q\nd955Z7ayKN2ScOnSpat0nH6xT38Iv/rqq+PjH//4KmVeECDQsUBarXnTTTfFAQcckH1vLVq0\naJUT0vdWum3djTfeGEOHDl2lzAsCBCojIH6pjKNWCPRU4I477oh99903+/9hy5Xvr7zySvzo\nRz/Kbnednrnqdsk9lXY+AQKNICB+aYRZdA2NICB+aYRZdA3NLiCBVIN3QLqN2c4771yDnnVZ\nLYGU6Lvrrrsi/dL+H//xH/Hwww9HWpabbr/1+c9/Pr70pS/FmmuuWa3utUugoQV23333eOGF\nF7I/jl144YXZJ6xT4mizzTbLPnG9//77R58+fRrawMURyIOA+CUPs2AMzSrw0EMPxV577ZXF\nl+0ZpIRS+rf33ntndznwTMD2lBwjQKAZBcQvzTjrrjkvAuKXvMyEcRDomYAEUs/8nE1gFYH0\nfKMNN9wwnnvuuex4+qN2+qSojQCBngmkX/xOOumk2GKLLeLdd9/NGttggw1iq6226lnDziZA\ngAABAnUgcPjhh2fPTe1sqOn/kaluuuuBjQABAgQIECBQSwHxSy319U2gcgKegVQ5Sy0RIECA\nAAECBAgQIECgogJpZftf/vKX7NmpnTWcnq/6yCOPxP33399ZVeUECBAgQIAAgaoJiF+qRqth\nAr0uIIHU6+Q6JECAAAECBAgQIECAQNcE7r777hg8eHDXKq+slZ6/mc6xESBAgAABAgRqJSB+\nqZW8fglUXkACqfKmWiRAgAABAgQIECBAgEBFBN54441YsWJFl9tKt7F7/fXXu1xfRQIECBAg\nQIBApQXEL5UW1R6B2glIINXOXs8ECBAgQIAAAQIECBDoUGDttdeO9FzNrm79+/ePdI6NAAEC\nBAgQIFArgXLjl379+olfajVZ+iXQiYAEUidAigkQIECAAAECBAgQIFArgZ133jkWLlzY5e5T\n3XSOjQABAgQIECBQK4Fy45dFixaJX2o1Wfol0ImABFInQIoJECBAgAABAgQIECBQK4GNN944\ndtlll0grizrbUp3tt98+Nt10086qKidAgAABAgQIVE1A/FI1Wg0T6HUBCaReJ9chAQIECBAg\nQIAAAQIEui5w4YUXxpAhQ6Jv39K/vqWyQYMGxUUXXdT1htUkQIAAAQIECFRJQPxSJVjNEuhl\ngdK/gfTyQHRHgAABAgQIECBAgAABAm0Fxo0bF3fddVess846WZKodY2UOErPGkh10id+bQQI\nECBAgACBWguIX2o9A/onUBkBCaTKOGqFAAECBAgQIECAAAECVROYMGFCPPPMM3H22WfH+PHj\nsxVJaVXSBz7wgfj2t78dzz77bHz4wx+uWv8aJkCAAAECBAiUKyB+KVdMfQL5E+j8Rtr5G7MR\nESBAgAABAgQIECBAoOkEBg8eHMccc0yWKHrjjTey6x8+fHjstNNOTWfhggkQIECAAIH6EBC/\n1Mc8GSWBUgJWIJWScZwAAQIECBAgQIAAAQIECBAgQIAAAQIECBAg0KQCEkhNOvEumwABAgQI\nECBAgAABAgQIECBAgAABAgQIECBQSkACqZSM4wQIECBAgAABAgQIECBAgAABAgQIECBAgACB\nJhWQQGrSiXfZBAgQIECAAAECBAgQIECAAAECBAgQIECAAIFSAhJIpWQcJ0CAAAECBAgQIECA\nAAECBAgQIECAAAECBAg0qYAEUpNOvMsmQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECJQSkEAq\nJeM4AQIECBAgQIAAAQIECBAgQIAAAQIECBAgQKBJBSSQmnTiXTYBAgQIECBAgAABAgQIECBA\ngAABAgQIECBAoJSABFIpGccJECBAgAABAgQIECBAgAABAgQIECBAgAABAk0qIIHUpBPvsgkQ\nIECAAAECBAgQIECAAAECBAgQIECAAAECpQQkkErJOE6AAAECBAgQIECAAAECBAgQIECAAAEC\nBAgQaFIBCaQmnXiXTYAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAoJSCBVErGcQIECBAgQIAA\nAQIECBAgQIAAAQIECBAgQIBAkwpIIDXpxLtsAgQIECBAgAABAgQIECBAgAABAgQIECBAgEAp\nAQmkUjKOEyBAgAABAgQIECBAgAABAgQIECBAgAABAgSaVEACqUkn3mUTIECAAAECBAgQIECA\nAAECBAgQIECAAAECBEoJSCCVknGcAAECBAgQIECAAAECBAgQIECAAAECBAgQINCkAhJITTrx\nLpsAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgUEpAAqmUjOMECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIAAgSYVkEBq0ol32QQIECBAgAABAgQIECBAgAABAgQIECBAgACBUgISSKVkHCdAgAAB\nAgQIECBAgAABAgQIECBAgAABAgQINKmABFKTTrzLJkCAAAECBAgQIECAAAECBAgQIECAAAEC\nBAiUEpBAKiXjOAECBAgQIECAAAECBAgQIECAAAECBAgQIECgSQUkkJp04l02AQIECBAgQIAA\nAQIECBAgQIAAAQIECBAgQKCUgARSKRnHCRAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQJNKiCB\n1KQT77IJECBAgAABAgQIECBAgAABAgQIECBAgAABAqUEJJBKyThOgAABAgQIECBAgAABAgQI\nECBAgAABAgQIEGhSAQmkJp14l02AAAECBAgQIECAAAECBAgQIECAAAECBAgQKCUggVRKxnEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECAQJMKSCA16cS7bAIECBAgQIAAAQIECBAgQIAAAQIE\nCBAgQIBAKQEJpFIyjhMgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIEmlRAAqlJJ95lEyBAgAAB\nAgQIECBAgAABAgQIECBAgAABAgRKCUgglZJxnAABAgQIECBAgAABAgQIECBAgAABAgQIECDQ\npAISSE068S6bAAECBAgQIECAAAECBAgQIECAAAECBAgQIFBKQAKplIzjBAgQIECAAAECBAgQ\nIECAAAECBAgQIECAAIEmFZBAatKJd9kECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAgVICEkil\nZBwnQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECDSpgARSk068yyZAgAABAgQIECBAgAABAgQI\nECBAgAABAgQIlBKQQCol4zgBAgQIECBAgAABAgQIECBAgAABAgQIECBAoEkFJJCadOJdNgEC\nBAgQIECAAAECBAgQIECAAAECBAgQIECglIAEUikZxwkQIECAAAECBAgQIECAAAECBAgQIECA\nAAECTSoggdSkE++yCRAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQKlBPqXKnCcQDUFHnzwwfjp\nT38ad911V7z11luxwQYbxL777huHHXZYrL766tXsWtsECBDIjcDbb78dF198cUyfPj2ef/75\nWG211eJjH/tYHH744fHhD384N+M0EAIECNSjwNy5c2PGjBnx6KOPxpIlS2KjjTaKyZMnZ1/r\n8XqMmQABAgQIECBAIF8Czz33XBZvPvXUUzFgwIDYdNNNs79vrr322vkaqNEQ6IGABFIP8Jxa\nvsDSpUvj6KOPjgsvvDD69esX6XXa0g/aP/zhD3HqqafG1VdfHXvssUf5jTuDAAECdSRw2223\nxUEHHRQLFy6MRYsWFUf+8MMPx3/913/FoYceGueff34MHDiwWGaHAAECBDoXWL58eZx55pnx\nzW9+M/r27ZvFm+nY4MGD4ytf+UpMmTIl+/nqQ0udW6pBgAABAgQIECDQViB9GPTII4+Myy+/\nPAYNGhSLFy+OPn36ZL+/f+lLX4oTTjghTj/99CwWbXu2IwTqS8At7Oprvup6tCtWrIj/83/+\nT1xyySWRfokvJI8KF5X+gDp//vzYe++94ze/+U3hsK8ECBBoOIE77rgj9txzz5g3b94qyaN0\noelnY/oZ+fOf/zw+9alPRfrZaSNAgACBrgkU4s2UPEqrjlJ8+e6772Y/S1PCPv18/cUvfhHb\nbbddtgq+a62qRYAAAQIECBAgQOA9gZQ8+sd//MfsA/AptizEmCnmTPvpd/qzzz479t9/f7/P\ne9M0hIAEUkNMY31cRMrK33TTTVlWvqMRpx+4Bx98cKQfyDYCBAg0mkAKKFMyPf2s62hLn2BK\nyfR0izsbAQIECHRN4Ic//GF2G5GUPCq1pZ+v6XYjRxxxRKkqjhMgQIAAAQIECBBoVyCtMHr6\n6ac7/PtmikVvueWWOPfcc9ttw0EC9SQggVRPs1XnYz3jjDOyT4J25TLSH1gvvfTSrlRVhwAB\nAnUlkFYWLViwoEtjTkFn+tlpI0CAAIHOBVJi/pRTTulSvJl+vl511VXZL/+dt6wGAQIECBAg\nQIAAgYhZs2bFZZdd1mHyqOCU4s2vf/3rbe7AVCj3lUC9CEgg1ctM1fk4X3311ew5R129jHS7\nkV/+8pddra4eAQIE6kbgV7/6VZvb1nU0+BSgvvjiix1VUUaAAAECKwXuueeeLifoE1i6X/2M\nGTPYESBAgAABAgQIEOiSQPpbZYohu7qlD8inZ77bCNSzgARSPc9eHY09/fEzPUyunO35558v\np7q6BAgQqAuBlBAqZ+vXr58EUjlg6hIg0LQCzzzzTPbg4q4CpA8spduP2AgQIECAAAECBAh0\nRSDFm2llUVe3gQMHxrPPPtvV6uoRyKWABFIup6XxBrXGGmuU/eC4YcOGNR6EKyJAoOkFhg8f\nXpZBuiVT+hlqI0CAAIGOBQYMGNBxhValffv2LSvh1Op0LwkQIECAAAECBJpMIMWb5X5Avn//\n/k2m5HIbTUACqdFmNKfXM27cuFh99dW7PLq0HHTHHXfscn0VCRAgUC8C6WdbOUvehw4dGhtv\nvHG9XJ5xEiBAoGYCm266aVm3CE2fCE3n2AgQIECAAAECBAh0RSDFjuUkhNKK980226wrTatD\nILcCEki5nZrGGlj6hOfnP//5Lv/RdOnSpXHooYc2FoKrIUCAwEqBqVOndvkhminRlH4WlhOg\nQiZAgECzCmy55Zax/vrrd/nyU7z5yU9+ssv1VSRAgAABAgQIEGhugcmTJ8fy5cu7jLDuuuvG\nNtts0+X6KhLIo4AEUg1mZcWKFTF79uxID1Kr9LZgwYLcPivj61//eqy55pqRnufR0ZY+DXrc\nccfF+PHjO6qmjAABAnUpsNFGG8UJJ5zQ6W2TUuI93bru9NNPr8vrNOjGE2jW+KXxZrKxr+gH\nP/hBp7FmEkjx5oknnhhrr712Y4O4OgIECDS5gPilyd8ALp9AhQVGjhwZp5xySqe/z6du098/\nU2xa7i3vKjxkzRHosYAEUo8Ju95AemjaIYccEul2RGPGjIn0jJ+JEyfGt771rbKfD9Sy15T5\nvuiii7JbHKXbxI0ePTrWW2+9OOigg+KRRx5pWbWm+yl5dPvtt8daa61VciVSupfowQcfHGef\nfXZNx6pzAgQIVFPgG9/4RnzmM58pubIorTwaNWpU9jMzfbURqKVAs8cvtbTXd/kCkyZNijPP\nPLPDJFJKHu29994S9OXzOoMAAQJ1IyB+qZupMlACdSfwta99Lfbdd98Ok0gpeXTqqafGfvvt\nV3fXZ8AEWgtIILUWqdLrlMjZeuut48orr8xWHm2yySYxZMiQmDlzZpx88snZLYqWLVvWrd7/\n5V/+Jbs93DPPPJM9Zyit3Hn55Zfj2muvzZ4jdM8993Sr3Wqc9KEPfSgef/zxOOaYY9o8FH6L\nLbaIq666Kn72s59F+uS9jQABAo0qkH7G/eQnP4lf/OIXkW651HJLHwT40pe+lP2s3HzzzVsW\n2SfQ6wLil14nr0mHv/71r7MPOaXnraUPIm2//fbx/e9/P9LK9nrcTjrppLjhhhtigw02yD7x\nmZLy6V/6RT6t7PzOd74T1113nXizHifXmAkQINAFAfFLF5BUIUCg2wLp9/mrr746zjnnnGxx\nQIoxC/FmWm2UFg2k3/VPO+20bvdRyxPffvvtOPfcc2OHHXbIfjdIvyNMmTIlbrnllloOS981\nFOhfw76bpuslS5ZE+jTk/PnzI/0xcMaMGTF27Nh4991347LLLosvfOELcemll0a6L+a3v/3t\nslwuuOCC7I+Q6QfU9773vSwxk35wpQRSWoF09913x+677x7PPfdc9mn2shqvUuXhw4dnK4w+\n97nPxR/+8IfsYccjRoyIAw88sMPsfZWGo1kCBAjUTCB9aukTn/hEXHPNNfHGG2/E4MGD45/+\n6Z881L1mM6LjlgLil5Ya7+2/+eabWRx37733ZnFdet7OHnvskX3ftq2d/yMpNk3x4h133JHd\ny71wP/cXX3wx7rvvvjjjjDPi+uuvj5133jn/F9NqhCn2Tv9SrH3//fdH+qBWmq9jjz225OrP\nVk14SYAAAQJ1KCB+qcNJM2QCdSiQ/g571FFHxRFHHJHdpi793TX9PXarrbaq62e633XXXdmq\nqXfeeSf7e21hatL1paTYjjvumC1YSHeZqsctLbK49dZb44UXXsg+WJYWe6S/y6S7hNlKC1jm\nUdqmYiWXXHJJPP/889mnHG+++eYseZQaTz9Y0sPRU8Y6bSkZVM5zkdIvwt/85jezc1MSKj03\nKLWZtve///2RPk2aPkWaPj2aPumety39sE23s0uZ+XRbPxsBAgSaVaBwa9P0M9EKzGZ9F+Tv\nusUvq85Jul1wukVwirnOO++8+OlPf5p98Cf9ErXddttFWgleT9vixYtjl112iTvvvDNLrhSS\nR4VrWLRoUZYkSx9ESh9IqtftAx/4QOy0006x6667Rlrt3r+/z8/V61waNwECBLoiIH7pipI6\nBAhUSiDFlmmxQIo104euPvjBD1aq6V5vJ90lK/1+MG/evFWSR2kg6XeF9HfotBAgxdbpd4V6\n2mbNmpU9RibdaSE9Sib9bpeeT5Xu6pV+x0t/k7eVFpBAKm1TsZKLL744ayv9MEkJndbb1KlT\ns5U36Rv0iiuuaF1c8nX6tGhKTKXtsMMOy762/E+6RV565lLazj///OybvWW5fQIECBAgQIBA\nKQHxy99lTj/99OzThelDOemXpUKyJSVh0oryBx54ID784Q/HE0888feTcr6XbuP26KOPRvqk\ndqktPXg8XV96PuXSpUtLVXOcAAECBAjkRkD8kpupMBACBOpIICWHUsyfYv/0O0CpLf3u8OST\nT2ZJmFJ18nb86aefzlaGpTsspOtLv8OlLe2n3+3SLfvSarJTTjklb0PPzXgkkKo8FekbK71B\n05buF9nelm7plm5/krbp06e3V6XdY3/605+y4+l2HOmWR+1t6Zs/bSnT+uCDD7ZXxTECBAgQ\nIECAwCoC4pe/c6QVOmeeeWb2ibu/H111L/3ClW7zMHny5OwXkVVL8/cqJcBSAqnwy1NHI0y/\nQL722mtlxagdtaeMAAECBAhUS0D8Ui1Z7RIg0OgCv/rVr7LHoXSUPCoYpN8h0mNU0u9Aed/S\n7z3pFnUpSdTReFNZeqzMb3/727xfUk3GJ4FUZfb0yc7CL+cbbrhhyd7GjRuXlT322GMl67Qu\nKCSmCue2Lk+vW5aV03Z7bTlGgAABAgQINIeA+OXv83zSSScVVxz9/WjbvfQJtrQyPN0bPO9b\n+lBRWk3V1S2tPkq3RrYRIECAAIE8C4hf8jw7xkaAQJ4FUuIk/T7T1S2t3EnPGc37duONN2a3\nGu8oeVS4hpRsOvHEEwsvfW0hIIHUAqMau3Pnzi02O2rUqOJ+650RI0Zkh2bPnt26qOTrQtsd\ntZtWNxWep1FO2yU7VUCAAAECBAg0vEAhxkgX2lGc0ejxy/z58yM9aLUrn8RLVukXk+uuuy7t\n5nqbM2dOdvvkrg4y/TKVHjRrI0CAAAECeRYQv+R5doyNAIE8C6QPwpWTQBowYEC2YinP15TG\nln4360ryKNVNv/OlxRqvv/56emlrIeApsi0wqrH75ptvFpsdOXJkcb/1TuEPMIX76heSPq3r\ntXxdaLujdlM7w4YNyx6Alpbrtd7SbVmOOeaY4uG05HvgwIHZvSG7Mobiid3YSX+MaPkHmdRf\nnz59utFSvk5pfV39+vXL1wC7OZpGva7W/4NslPlqeV3p+6ra38/dfFuVfVojXlf6OZi+vwpb\nb81XenjkrbfeWujWVwKrCBRijHSwozij0eOX1v/vWwWpnRep/jXXXBMzZsxopzQ/h9LP0sIK\n+a6O6rbbbouhQ4d2tXpu6rWew0b8/3zCbsTr6q3/H/bGm1X8Ujll8UvlLBuxJfFL6Vlt/f9D\nf38pbZWHktbz1Yj/n0/OjXhd9Rq/pL8Hl7Olv1+nx6bkfQ4Lf2cv59pGjx5d8b+h1Xv8IoFU\nzjuoG3VbJm3WXHPNki2kJE9hS2/uIUOGFF6W/Fpou6N208mFBFJqt/WW+tlggw1WObzZZpvF\nU089tcoxLwgQIECgsQTWW2+9xrogV1NRgUKMkRrtKM4Qv1SUXWMECBAg0ImA+KUToCYvFr80\n+RvA5RMgQCCnAvUev0ggVfmN1fJTu+le84MHD263x8J96FOmulSd1iemtmfNmtXpPewLbbeX\nlNpuu+0i3Q/SRoAAAQIECBAoCIhfChK+EiBAgAABAvUiIH6pl5kyTgIECBCoJwHPQKrybK27\n7rrFHt54443ifuudQtlqq63W5WVyhbYL57ZuM71Ot0aaN29eVrTGGmu0V8UxAgQIECBAgMAq\nAoUYIx3sKM4olIlfVuHzggABAgQIEKiBgPilBui6JECAAIGGF5BAqvIUlxvAFJ4l0JVhFdou\n/PGmvXPSPYAL99wup+322nKMAAECBAgQaA6BQoyRrrajOKNQVk6MUWi7cG57ouKX9lQcI0CA\nAAECBDoSKMQYqU5HcUahTPzSkaYyAgQIECDwnoAEUpXfCWuvvXbxgWIvvvhiyd4KZVtuuWXJ\nOq0LCsFR4dzW5el1y7Jy2m6vLccIECBAgACB5hAQvzTHPLtKAgQIECDQSALil0aaTddCgAAB\nAnkRkECq8kz07ds3tt1226yX66+/vt3eFi5cGLfccktWNnHixHbrtHfwIx/5SHb4kUceiaee\neqq9KlHoMz3/aIsttmi3joMECBAgQIAAgZYC4peWGvYJECBAgACBehAQv9TDLBkjAQIECNSb\ngARSL8zYcccdl/Vyww03xIIFC9r0OH369HjrrbeyZx8deOCBbcpLHdhzzz1j0003zYovv/zy\nNtXS848Kxw844IDo379/mzoOECBAgAABAgTaExC/tKfiGAECBAgQIJBnAfFLnmfH2AgQIECg\nHgUkkHph1lJSaOzYsfH222/HPvvskyWLCt3OnDkzjjzyyOzlQQcdFJtsskmhKPuaEkvpePr3\n4x//eJWyPn36xPHHH58d++Y3vxnXXnttsTw99+jQQw+Nxx9/PEtMnXDCCcUyOwQIECBAgACB\nzgTEL50JKSdAgAABAgTyJiB+yduMGA8BAgQI1LtAn5WrVFbU+0XUw/hnzJgRU6ZMiXfeeSeG\nDx8eO+ywQ8ydOzfuvffeWLZsWYwfPz7++Mc/RuuHOL7++usxatSo7BL/9V//NX70ox+tcrmL\nFy+OSZMmxW9/+9tICaV0m7qUhLr77rtjzpw5Wd3//M//jKOOOmqV87wgQIAAAQIECHQmIH7p\nTEg5AQIECBAgkDcB8UveZsR4CBAgQKCeBaxA6qXZmzx5cpYgmjBhQsyfPz9SQHPPPffE8uXL\nY+rUqXH77be3SR51ZWiDBg3Knp+UVhgNHTo0HnroofjFL36RJY822GCD+PnPfy551BVIdQgQ\nIECAAIE2AuKXNiQOECBAgAABAjkXEL/kfIIMjwABAgTqSsAKpBpM19/+9rd44IEHYuDAgdnK\no5EjR1ZkFCkZ9eSTT8bzzz8fY1feMm+jjTby3KOKyGqEAAECBAgQEL94DxAgQIAAAQL1JiB+\nqbcZM14CBAgQyJuABFLeZsR4CBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQI1FnALuxpPgO4J\nECBAgAABAgQIECBAgAABAgQIECBAgAABAnkTkEDK24wYDwECBAgQIECAAAECBAgQIECAAAEC\nBAgQIECgxgISSDWeAN0TIECAAAECBAgQIECAAAECBAgQIECAAAECBPImIIGUtxkxHgIECBAg\nQIAAAQIECBAgQIAAAQIECBAgQIBAjQUkkGo8AbonQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCORNQAIpbzNiPAQIECBAgAABAgQIECBAgAABAgQIECBAgACBGgtIINV4AnRPgAABAgQIECBA\ngAABAgQIECBAgAABAgQIEMibgARS3mbEeAgQIECAAAECBAgQIECAAAECBAgQIECAAAECNRaQ\nQKrxBOieAAECBAgQIECAAAECBAgQIECAAAECBAgQIJA3AQmkvM1IE41nxYoVMXv27Fi4cGET\nXXV9X+pLL70Ur732Wn1fRBOO/p133olXX3010ldbfgVeeeWVmDdvXn4HaGQECGQC4pf6eyOI\nX+pvztKIxS/1MW/il/qYJ6MkIH6pv/eA+KX+5iyNWPxSH/MmfilvniSQyvNSuwICzz77bBxy\nyCExdOjQGDNmTAwbNiwmTpwY3/rWtyIFNbZ8Cfzud7+LHXfcMVZbbbVYb731Yq211oqRI0fG\nJz/5yXjyySfzNVijaSOwaNGi2G677eJ973tf/Od//mebcgdqK/DYY4/F/vvvH6NHj4511lkn\nRowYkc3VaaedJuFX26nRO4E2AuKXNiS5PiB+yfX0dDo48UunRDWtIH6pKb/OCZQlIH4pi6vm\nlcUvNZ+CHg1A/NIjvqqfLH7pAfHKP9jbCPSawMMPP7xiZcIoZYmyf5tssskqr6dOnbpi6dKl\nvTYeHXUsMG3atOJc9e/ff8UHP/jBFWPHjl3Rp0+f7PjAgQNX/OxnP+u4EaU1FTjmmGOKc3jW\nWWfVdCw6X1XgqquuWrEyMVucnw984AMrViZoi6+32mqrFSs/vbTqSV4RIFATAfFLTdi73an4\npdt0uTlR/JKbqWgzEPFLGxIHCORWQPyS26lpd2Dil3ZZ6uqg+CW/0yV+6dncWIHUg+SbU8sT\nWLJkSUyaNCnmz58fm2++eTz33HPZCpbXX389Lr744liZoIhLL700TjnllPIaVrsqAtOnT4/v\nfve7Wdtf/OIXI83T448/Xpy37bffPtKcHnnkkfHUU09VZQwa7ZnArbfeGj/4wQ961oizqyLw\n0EMPxcEHHxwLFiworuZ74oknslsNpp+HK5Oz8cADD8RXv/rVqvSvUQIEui4gfum6VR5qil/y\nMAs9G4P4pWd+1Txb/FJNXW0TqKyA+KWyntVuTfxSbeHqty9+qb5xd3sQv3RXrsV5Pcs/OZtA\n1wUuuOCC7JP1ffv2XfHXv/61zYnnnXdeVr7mmmv61H0bnd4/sPK2Z9l87Lrrru12vjKhtGLl\nLbeyOkcddVS7dRysncDKZ1WteP/7378ifb8NGjQomycrkGo3H617/ud//udsTjbaaKMVK5Pq\nrYtXHHbYYVn58OHDrcpso+MAgd4VEL/0rndPexO/9FSwtueLX2rr31nv4pfOhJQTyI+A+CU/\nc9GVkYhfuqKU3zril/zOTRqZ+KXn82MFUotkmt3qCqRP1adtZUIie95H9qLFf1bevi771H16\niPwVV1zRosRubwu89dZbcf/992fdptVH7W3pWS177bVXVlSo2149x2ojkObt5ZdfjuOPPz57\npk5tRqHX9gTS6suVy6djZXIv+7rGGmu0qZbmbY899oi999475syZ06bcAQIEek9A/NJ71j3t\nSfzSU8Hany9+qf0clBqB+KWUjOME8ikgfsnnvLQ3KvFLeyr1dUz8kt/5Er9UZm4kkCrjqJVO\nBNLy6fvuuy+rNWXKlHZrr/ykffYH01SYlu/aaieQ5uucc86JE044ISZOnFhyICtXtmRlb7/9\ndsk6Cnpf4KKLLorrr78+tthii/jGN77R+wPQY4cC6Vad7777bqx8xlFss8027dZNc5eWwF9+\n+eXtJtzbPclBAgQqLiB+qThpVRsUv1SVt+qNi1+qTtyjDsQvPeJzMoFeFRC/9Cp3jzsTv/SY\nsKYNiF9qyt9p5+KXTom6VKF/l2qpRKCHAo8++mgsXrw4a2XDDTcs2dq4ceOysscee6xkHQXV\nFxg5cmSsfPhfhx0tX7487rzzzqzOtttu22Fdhb0n8Mwzz8SXv/zlbDVf+h9lIcnXeyPQU2cC\nzz//fFZlp512KlZNSdg//elPkb6vtt566xg1alSxzA4BArUTEL/Uzr47PYtfuqOWj3PEL/mY\nh45GIX7pSEcZgXwJiF/yNR+djUb80plQfsvFL/mdm8LIxC8FiZ59tQKpZ37O7qLA3LlzizU7\n+sNoui1a2mbPnl2sbyefApdcckn87//+bza4SZMm5XOQTTaqtKrlM5/5TCxYsCDOPPPM2HLL\nLZtMoD4ut/Dzbb311ouV90qOPffcM9IKzN133z3bX2uttWK//fbLyurjioySQOMKiF8ab27F\nL/mbU/FL/uakvRGJX9pTcYxAPgXEL/mcl56MSvzSE73qnCt+qY5rpVsVv1RGVAKpMo5a6UTg\nzTffLNZIn64otRUSSIsWLco+iV+qnuO1FUi3IyysUEp/6N5///1rOyC9ZwLpdnX33HNP7LDD\nDjFt2jQqORV48cUXs5GlVUdprn7961/Huuuumz0fbv3118/K0m08J0yYIJme0zk0rOYREL80\n1lyLX/I5n+KXfM5L61GJX1qLeE0gvwLil/zOTXdGJn7pjlr1zxG/VN+4Ej2IXyqhGCGBVBlH\nrXQi0PIZOWuuuWbJ2sOGDSuWpSSSLX8CadXRJz7xiWyVy9prrx3nn39+/gbZhCNKiaMUwKy+\n+urxs5/9LPr29eM9r2+DQgBzxhlnxEsvvRRXXnllpGXVv/3tb7Ovl112WQwdOjRefvnlYqI2\nr9diXAQaXUD80jgzLH7J51yKX/I5L+2NSvzSnopjBPIpIH7J57x0Z1Til+6oVf8c8Uv1jSvV\ng/ilMpL+wlgZR610ItBy1VG6vVaprVDWp0+fGDx4cKlqjtdI4A9/+EN87GMfi7QkPt1m67bb\nbov3ve99NRqNbgsC6ftm6tSpsWzZsjj33HNj7NixhSJfcyiQ5iltacn7f/zHf8TBBx+8yig/\n/elPx+mnn54du/766yN94sxGgEBtBMQvtXGvdK/il0qLVqY98UtlHHurFfFLb0nrh0DPBcQv\nPTfMQwvilzzMQtsxiF/amuT5iPilMrMjgVQZR610IpBuz1TY3njjjcJum6+FstVWW80KijY6\ntT1wzTXXxG677RZpjtJttn73u9/F5ptvXttB6T0TOPbYY+Ppp5/Onptz+OGHU8m5wOjRo7MR\npiRsqfk6+uijo3///lm9v/zlLzm/IsMj0LgC4pf6n1vxS37nUPyS37lpb2Til/ZUHCOQTwHx\nSz7npZxRiV/K0erduuKX3vXuaW/il54Kvnf+e3+dqkxbWiFQUqDcAKbwLKSSDSroVYHvfve7\n8W//9m+xYsWK2GqrreJXv/pV9syWXh2EztoVePbZZ+MnP/lJVpZuh7bXXnu1qffqq69mx1K9\n22+/PdtPz9gZNGhQm7oOVF8gBTDpVgQf+tCHSnaW5iatJEuJwVTXRoBAbQTEL7Vxr1Sv4pdK\nSVa+HfFL5U2r3aL4pdrC2idQOQHxS+Usa9GS+KUW6l3rU/zSNac81RK/VGY2JJAq46iVTgTS\ns3L69euX3bKpcP/J9k4plG255ZbtFTtWA4Evf/nLcd5552U9p2cfXXXVVdlzdmowFF22I7B4\n8eLi0f/5n/8p7re38+STT0b6l7Z0+zRbbQQKn4CZM2dOhwMozNF6663XYT2FBAhUT0D8Uj3b\narcsfqm2cM/aF7/0zK8WZ4tfaqGuTwLdExC/dM8tD2eJX/IwC6XHIH4pbZPXEvFLZWZGAqky\njlrpRKBv376x7bbbxsyZMyM90+OAAw5oc8bChQvjlltuyY5PnDixTbkDvS8wbdq0YvLoiCOO\niP/6r//KEoG9PxI9lhJYZ511inNUqs5pp50W8+bNi3333Te7DWGqN3DgwFLVHa+ywNZbbx0X\nX3xxlsx7/fXXo+U9ygtdp5+Hzz//fPYyPXfMRoBAbQTEL7Vx72mv4peeClb/fPFL9Y0r3YP4\npdKi2iNQPQHxS/Vsq9my+KWaupVpW/xSGcfebEX8UiHtlbekshHoFYErr7xyxcq37YqhQ4eu\neOutt9r0ecUVV2TlK4OdFStXSbQpd6B3BW6++eZsPtKcrfwUTO92rreKCqx8ZlU2l2eddVZF\n29VY9wTefvvtFaNGjcrm5MQTT2y3kbPPPjsrHzJkyIolS5a0W8dBAgR6R0D80jvOlepF/FIp\nydq3I36p/Ry0HIH4paWGfQL5FxC/5H+OWo5Q/NJSo773xS/5mj/xS2XmwwqkCiXiNNO5wIEH\nHpg902PWrFmxzz77xC9/+cvirdDSyqQjjzwya+Sggw6KTTbZpPMG1aiaQFqW+3//7//N2t9g\ngw1i0qRJ8bvf/a5kfwMGDAirJEryKCCwisDKpFAcf/zxcfLJJ8e3v/3tWBlgRlrhlz4pmLb0\nfKozzjgj2//qV78a6fvLRoBA7QTEL7WzL7dn8Uu5YuoT6LqA+KXrVmoSyIOA+CUPs9C1MYhf\nuuakFoHuCIhfuqPW9pw+KQ/V9rAjBKojMGPGjJgyZUq88847MXz48Nhhhx1i7ty5ce+998ay\nZcti/Pjx8cc//jFGjBhRnQFotUsC559/fjGh15UT0i24Xnvtta5UVacGAikJ+MILL8TKFUjx\nb//2bzUYgS5bC6SfgYcffnhcffXVWdFaa60VO+64Y6QE+3333Zcd+8IXvhA//vGPW5/qNQEC\nNRAQv9QAvRtdil+6gZbjU8Qv+Zsc8Uv+5sSICHQkIH7pSCc/ZeKX/MxFJUYifqmEYmXbEL/0\n3PO9jzv3vB0tEOiSwOTJk7ME0YQJE2L+/PmRApp77rknli9fHlOnTo3bb79d8qhLktWtVPgD\ndnV70TqB5hVIn4K56qqrsudXrbfeelki/Re/+EWWPFp5m8849thjI/0iYSNAIB8C4pd8zENn\noxC/dCaknEDPBMQvPfNzNoHeFhC/9LZ49/oTv3TPzVkEuiogfumqVOl6ViCVtlFSZYG//e1v\n8cADD8TAgQOzlUftPUi+ykPQPAECBHIhMGfOnHjooYdi2LBhsemmmxZv75mLwRkEAQKrCIhf\nVuHwggCBJhYQvzTx5Lv0uhMQv9TdlBkwAQJVEhC/lA8rgVS+mTMIECBAgAABAgQIECBAgAAB\nAgQIECBAgAABAg0t4BZ2DT29Lo4AAQIECBAgQIAAAQIECBAgQIAAAQIECBAgUL6ABFL5Zs4g\nQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECDS0gARSQ0+viyNAgAABAgQIECBAgAABAgQIECBA\ngAABAgQIlC8ggVS+mTMIECBAgAABAgQIECBAgAABAgQIECBAgAABAg0tIIHU0NPr4ggQIECA\nAAECBAgQIECAAAECBAgQIECAAAEC5QtIIJVv5gwCBAgQIECAAAECBAgQIECAAAECBAgQIECA\nQEMLSCA19PS6OAIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBA+QISSOWbOYMAAQIECBAgQIAA\nAQIECBAgQIAAAQIECBAg0NACEkgNPb0ujgABAgQIECBAgAABAgQIECBAgAABAgQIECBQvoAE\nUvlmziBAgAABAgQIECBAgAABAgQIECBAgAABAgQINLSABFJDT6+LI0CAAAECBAgQIECAAAEC\nBAgQIECAAAECBAiULyCBVL6ZMwgQIECAAAECBAgQIECAAAECBAgQIECAAAECDS0ggdTQ0+vi\nCBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQLlC/Qv/xRnECBAoP4EnnvuuZg8eXJx4DvssEP8\n6Ec/Kr4u7LzzzjvxsY99LJYuXZod+shHPhIXXXRRodhXAgQIECBAgECvCYhfeo1aRwQIECBA\ngECFBMQvFYLUDIGcCEgg5WQiDIMAgeoKjBs3Lvr37x8PPvhg1tEzzzwTZ511VqyxxhqrdHzz\nzTfHAw88UDx21FFHFfftECBAgAABAgR6U0D80pva+iJAgAABAgQqISB+qYSiNgjkR8At7PIz\nF0ZCgECVBQ4//PBiD4sWLYobb7yx+Lqwc+211xZ2Y+DAgXHwwQcXX9shQIAAAQIECPS2gPil\nt8X1R4AAAQIECPRUQPzSU0HnE8iPgARSfubCSAgQqLLApz/96SwpVOjm6quvLuxmX1NS6Ze/\n/GXx2KRJk2LEiBHF13YIECBAgAABAr0tIH7pbXH9ESBAgAABAj0VEL/0VND5BPIjIIGUn7kw\nEgIEqiwwatSoVZ6D9Otf/zrmz59f7PXWW2+NBQsWFF9/9rOfLe7bIUCAAAECBAjUQkD8Ugt1\nfRIgQIAAAQI9ERC/9ETPuQTyJSCBlK/5MBoCBKos0HIZ9eLFi2P69OnFHq+55pri/siRI2Pv\nvfcuvrZDgAABAgQIEKiVgPilVvL6JUCAAAECBLorIH7prpzzCORLQAIpX/NhNAQIVFlgr732\nive///3FXgq3sUvJpBkzZhSPT5kyJQYMGFB8bYcAAQIECBAgUCsB8Uut5PVLgAABAgQIdFdA\n/NJdOecRyJeABFK+5sNoCBCoskC/fv1i6tSpxV5+85vfxLx58yJ9ffPNN4vH3b6uSGGHAAEC\nBAgQqLGA+KXGE6B7AgQIECBAoGwB8UvZZE4gkEsBCaRcTotBESBQTYHDDjus2PySJUvihhtu\niGuvvbZ47IMf/GB85CMfKb62Q4AAAQIECBCotYD4pdYzoH8CBAgQIECgXAHxS7li6hPIn4AE\nUv7mxIgIEKiywIc+9KGYOHFisZfLLrtslWchtVyhVKxkhwABAgQIECBQQwHxSw3xdU2AAAEC\nBAh0S0D80i02JxHIlUCfFSu3XI3IYAgQINALAhdccEEcccQRbXrq06dPzJo1K9Zff/02ZQ4Q\nIECAAAECBGopIH6ppb6+CRAgQIAAge4IiF+6o+YcAvkRkEDKz1wYCQECvSgwf/78eP/73x8L\nFy5cpdePf/zjcfvtt69yzAsCBAgQIECAQB4ExC95mAVjIECAAAECBMoREL+Uo6UugfwJuIVd\n/ubEiAgQ6AWBYcOGxac+9ak2PX32s59tc8wBAgQIECBAgEAeBMQveZgFYyBAgAABAgTKERC/\nlKOlLoH8CViBlL85MSICBHpJ4Lbbbovddtut2NuQIUNizpw5sfrqqxeP2SFAgAABAgQI5ElA\n/JKn2TAWAgQIECBAoCsC4peuKKlDIJ8CViDlc16MigCBXhBYunTpKr3st99+kkeriHhBgAAB\nAgQI5E1A/JK3GTEeAgQIECBAoDMB8UtnQsoJ5FdAAim/c2NkBAhUWeCMM85YpYfPfOYzq7z2\nggABAgQIECCQNwHxS95mxHgIECBAgACBzgTEL50JKSeQXwG3sMvv3BgZAQIVFnjooYfiL3/5\nS7z66qtx4YUXxpNPPlnsYdNNN42HH344+vaVVy+i2CFAgAABAgRqLiB+qfkUGAABAgQIECBQ\npoD4pUww1QnkWKB/jsdmaAQIEKiowNNPPx2HHXZYu22efvrpkkftyjhIgAABAgQI1FJA/FJL\nfX0TIECAAAEC3REQv3RHzTkE8ingo/b5nBejIkCgCgJjxoxp02r//v3jm9/8Zhx44IFtyhwg\nQIAAAQIECNRaQPxS6xnQPwECBAgQIFCugPilXDH1CeRXwC3s8js3RkaAQIUF3nrrrfjv//7v\nePHFF6Nfv34xduzY2G+//WL06NEV7klzBAgQIECAAIHKCIhfKuOoFQIECBAgQKD3BMQvvWet\nJwLVFpBAqraw9gkQIECAAAECBAgQIECAAAECBAgQIECAAAECdSbgFnZ1NmGGS4AAAQIECBAg\nQIAAAQIECBAgQIAAAQIECBCotoAEUrWFtU+AAAECBAgQIECAAAECBAgQIECAAAECBAgQqDMB\nCaQ6mzDDJUCAAAECBAgQIECAAAECBAgQIECAAAECBAhUW0ACqdrC2idAgAABAgQIECBAgAAB\nAgQIECBAgAABAgQI1JmABFKdTZjhEiBAgAABAgQIECBAgAABAgQIECBAgAABAgSqLSCBVG1h\n7RMgQIAAATRiw+gAAAVlSURBVAIECBAgQIAAAQIECBAgQIAAAQIE6kxAAqnOJsxwCRAgQIAA\nAQIECBAgQIAAAQIECBAgQIAAAQLVFpBAqraw9gkQIECAAAECBAgQIECAAAECBAgQIECAAAEC\ndSYggVRnE2a4BAgQIECAAAECBAgQIECAAAECBAgQIECAAIFqC0ggVVtY+wQIECBAgAABAgQI\nECBAgAABAgQIECBAgACBOhOQQKqzCTNcAgQIECBAgAABAgQIECBAgAABAgQIECBAgEC1BSSQ\nqi2sfQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAnQlIINXZhBkuAQIECBAgQIAAAQIECBAg\nQIAAAQIECBAgQKDaAhJI1RbWPgECBAgQIECAAAECBAgQIECAAAECBAgQIECgzgQkkOpswgyX\nAAECBAgQIECAAAECBAgQIECAAAECBAgQIFBtAQmkagtrnwABAgQIECBAgAABAgQIECBAgAAB\nAgQIECBQZwISSHU2YYZLgAABAgQIECBAgAABAgQIECBAgAABAgQIEKi2gARStYW1T4AAAQIE\nCBAgQIAAAQIECBAgQIAAAQIECBCoMwEJpDqbMMMlQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE\nCFRbQAKp2sLaJ0CAAAECBAgQIECAAAECBAgQIECAAAECBAjUmYAEUp1NmOESIECAAAECBAgQ\nIECAAAECBAgQIECAAAECBKotIIFUbWHtEyBAgAABAgQIECBAgAABAgQIECBAgAABAgTqTEAC\nqc4mzHAJECBAgAABAgQIECBAgAABAgQIECBAgAABAtUWkECqtrD2CRAgQIAAAQIECBAgQIAA\nAQIECBAgQIAAAQJ1JiCBVGcTZrgECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAgWoLSCBVW1j7\nBAgQIECAAAECBAgQIECAAAECBAgQIECAAIE6E5BAqrMJM1wCBAgQIECAAAECBAgQIECAAAEC\nBAgQIECAQLUFJJCqLax9AgQIECBAgAABAgQIECBAgAABAgQIECBAgECdCUgg1dmEGS4BAgQI\nECBAgAABAgQIECBAgAABAgQIECBAoNoCEkjVFtY+AQIECBAgQIAAAQIECBAgQIAAAQIECBAg\nQKDOBCSQ6mzCDJcAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgUG0BCaRqC2ufAAECBAgQIECA\nAAECBAgQIECAAAECBAgQIFBnAhJIdTZhhkuAAAECBAgQIECAAAECBAgQIECAAAECBAgQqLaA\nBFK1hbVPgAABAgQIECBAgAABAgQIECBAgAABAgQIEKgzAQmkOpswwyVAgAABAgQIECBAgAAB\nAgQIECBAgAABAgQIVFtAAqnawtonQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECNSZgARSnU2Y\n4RIgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIEqi0ggVRtYe0TIECAAAECBAgQIECAAAECBAgQ\nIECAAAECBOpMQAKpzibMcAkQIECAwP9vz45JAAAAEAj2b22KH4QrIHKOEiBAgAABAgQIECBA\ngAABAgQIECBQCziQamH5BAgQIECAAAECBAgQIECAAAECBAgQIECAAIEzAQfS2WDqEiBAgAAB\nAgQIECBAgAABAgQIECBAgAABAgRqAQdSLSyfAAECBAgQIECAAAECBAgQIECAAAECBAgQIHAm\n4EA6G0xdAgQIECBAgAABAgQIECBAgAABAgQIECBAgEAt4ECqheUTIECAAAECBAgQIECAAAEC\nBAgQIECAAAECBM4EHEhng6lLgAABAgQIECBAgAABAgQIECBAgAABAgQIEKgFBjYW2tjOWdE6\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 绘制三个子图，每个子图对应不同的成功概率\n",
    "plots <- list()\n",
    "titles <- c(\"Team itself(π = 0.5)\", \"Optimists(π = 0.8)\", \"Pessimists(π = 0.2)\")\n",
    "\n",
    "for (i in 1:length(p_values)) {\n",
    "  plots[[i]] <- ggplot(data.frame(y = y, likelihood = likelihoods[,i]), aes(x = y, y = likelihood)) +\n",
    "    geom_segment(aes(xend = y, yend = 0), color = \"gray\", size = 1) +\n",
    "    geom_point(color = \"black\", size = 3) +\n",
    "    labs(title = titles[i], x = 'y', y = 'f(y | π)') +\n",
    "    xlim(-0.2, 6.2) +\n",
    "    scale_y_continuous(expand = c(0,0),limits = c(0, 0.45)) + \n",
    "    APA_theme\n",
    "}\n",
    "\n",
    "# 将三个图以子图的形式并排显示\n",
    "options(repr.plot.width=14, repr.plot.height=5) #自定义画布大小\n",
    "grid.arrange(grobs = plots, ncol = 3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8cb49ff",
   "metadata": {
    "_id": "ECAB551A37B54158AC2B5734427CAD1E",
    "id": "82230022EA50413AAFD002E5BFB55B70",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "显然，对于乐观派来说，团队取得六次成功的概率远高于其他成功次数。而对于悲观派来说，团队全败的可能性远高于其他成功次数。  \n",
    "- 换句话说，若团队在6项研究中仅成功复现一次，这种情况在低成功率下(悲观派设想的情境)更可能出现，在高成功率下(乐观派设想的情境)几乎不可能出现。  \n",
    "- 那么团队成功重复的成功率率，更可能(likelihood)是悲观派设想的那样($\\pi = 0.2$)。  \n",
    "\n",
    "例如，在乐观派和悲观派眼中(不同成功率$\\pi$下)，6项研究只成功1次的可能性(即似然，likelihood)。  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "aaa966b3",
   "metadata": {
    "_id": "44F114058962412AAEEF8D6DA01A1FB8",
    "collapsed": false,
    "id": "E16BAF3537A646D697966C6B0B29AB11",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5fWVGlF/s/a\n24Nf3ZwjweV5n7iAfQ5EexIhv8MTc+ZR3on5eaa0Bs7W3fLmx5qaqHDixImF1nhW84Gpj2r9\n9NNPi7XVevqU2f7nP/+5yDbrRrLCli1bmm36yO5HH3200JovtNC6scSsC36ks13QTRm7LK/O\nBdx4W1eVAueDvcdjx44VVqlSxazX88eaWSXijwbGdtJHuls3Iply1td/hQ8//LD5sYZsmHX6\nGGBrqiw7O68JCiSrv/UwtK7rrrsu0OfWeFjz2OC8vDzTpxo8P/vss8WO2M1nTLFKWBGXQDL7\n296h9ql1La/Quvpsr4r46vYciVghGxwLxBNA8zvcMWuRAgTQRTj8vWDd9FVo/4fSD0r9sWZL\nKFy5cmVYGDtvaACtmTWw6t+/f6H12G5Tj9alVy5GjhxZaE1jF7Y+N2XCVsTKuASceocLoK35\nfwP9a58zkV6tMdJFjst66EahBsrB+a2ZXgqHDBlSeOLEiSJ5WUhcIBn9bR+FfotgPQTH/J+2\n+0//ILryyisLly1bZmcr9ur0M6ZYBayIWyCZ/a07tb+NjPebIbfnSNwNJGNUgUQCaK3Y6fnj\ntkzURmT4xhw9PusDkIRAQEAnyd+6datYAbLo3dI6ZZHbpGOo169fb+rQR/9WqFAhZlVuysSs\nlAwRBc63tz6IQ294qlatmnmUdyLnW8RGsiEgkMz+tq40mnHs2oc6/eCFF14Y2E+0N8n8jIm2\nH7aJJLO/3Xi6PUfc7IsyyRdwc/64KZP8I099jQTQqTdmDwgggAACCCCAAAIeEmAWDg91Jk1B\nAAEEEEAAAQQQSL0AAXTqjdkDAggggAACCCCAgIcECKA91Jk0BQEEEEAAAQQQQCD1AgTQqTdm\nDwgggAACCCCAAAIeEiCA9lBn0hQEEEAAAQQQQACB1AsQQKfemD0ggAACCCCAAAIIeEiAANpD\nnUlTEEAAAQQQQAABBFIvQACdemP2gAACCPhCQJ/LxbO5fNHVNBIB3wvk+l4AAAQQQACBqAIa\nFL///vvmCaWHDh2S0qVLywUXXGBeS5UqJfpz8uRJeeONN+TZZ5+VBg0aRK2PjQgggEC2CxBA\nZ3sPcvwIIIBACgXOnDkjnTt3lo8++ijmXjp16kTwHFOJDAgg4AUBAmgv9CJtQAABBFIk8MEH\nH0jJkiVl0aJF8vnnn8vx48elT58+UlBQIGPGjDHrf/nLX8qvf/1radq0aYqOgmoRQACBzBIg\ngM6s/uBoEEAAgYwSuPjii83QjBo1asiOHTukSpUq0rx5c3OMlStXNq/XXHMNwXNG9RoHgwAC\nqRYggE61MPUjgAACWSxwxRVXBI5erz5fdNFFgWW9Cq1Jx0STEEAAAT8JMAuHn3qbtiKAAAIJ\nCBw7dkzKlSsXqMEOoPUmQhICCCDgJwECaD/1Nm1FAAEEEhDYuXOnXHjhhYEazp07Z97rGGkS\nAggg4CcBAmg/9TZtRQABBBIQ2LJli9SsWTNQQ8WKFc17O5BeuXKl5OfnB7bzBgEEEPCqAAG0\nV3uWdiGAAAJJEBg9erTo3M9bt26Vjz/+WBo2bBio1b4arXNAa5o9e7acPXs2sJ03CCCAgFcF\nuInQqz1LuxBAAIEkCNSpU0fat28ve/bskWbNmkm1atUCtbZo0cK8//LLL+Xw4cMmyNbZOkgI\nIICA1wW4Au31HqZ9CCCAQAICN9xwg/zwww9y4sQJ+dOf/lSkpltuuUWaNGkiTzzxhDRq1Ej6\n9esnJUrwa6UIEgsIIOBJgRzrEa2FnmwZjUIAAQQQSIqATl+nwzR0DujQpE8q3Lx5s9SuXTvs\n9tD8LCOAAAJeECCA9kIv0gYEEEAAAQQQQACBtAnwXVvaqNkRAggggAACCCCAgBcECKC90Iu0\nAQEEEEAAAQQQQCBtAgTQaaNmRwgggAACCCCAAAJeECCA9kIv0gYEEEAAAQQQQACBtAkQQKeN\nmh0hgAACCCCAAAIIeEGAANoLvUgbEEAAAQQQQAABBNImQACdNmp2hAACCCCAAAIIIOAFAQJo\nL/QibUAAAQQQQAABBBBImwABdNqo2RECCCCAAAIIIICAFwQIoL3Qi7QBAQQQQAABBBBAIG0C\nBNBpo2ZHCCCAAAIIIIAAAl4QIID2Qi/SBgQQQAABBBBAAIG0CRBAp42aHSGAAAIIIIAAAgh4\nQYAA2gu9SBsQQAABBBBAAAEE0iZAAJ02anaEAAIIIIAAAggg4AUBAmgv9CJtQAABBBBAAAEE\nEEibAAF02qjZEQIIIIAAAggggIAXBAigvdCLtAEBBBBAAAEEEEAgbQIE0GmjZkcIIIAAAggg\ngAACXhAggPZCL9IGBBBAAAEEEEAAgbQJEECnjZodIYAAAggggAACCHhBgADaC71IGxBAAAEE\nEEAAAQTSJkAAnTZqdoQAAggggAACCCDgBQECaC/0Im1AAAEEEEAAAQQQSJsAAXTaqNkRAggg\ngAACCCCAgBcECKC90Iu0AQEEEEAAAQQQQCBtAgTQaaNmRwgggAACCCCAAAJeECCA9kIv0gYE\nEEAAAQQQQACBtAkQQKeNmh0hgAACCCCAAAIIeEGAANoLvUgbEEAAAQQQQAABBNImQACdNmp2\nhAACCCCAAAIIIOAFAQJoL/QibUAAAQQQQAABBBBImwABdNqo2RECCCCAAAIIIICAFwQIoL3Q\ni7QBAQQQQAABBBBAIG0CBNBpo2ZHCCCAAAIIIIAAAl4QIID2Qi/SBgQQQAABBBBAAIG0CRBA\np42aHSGAAAIIIIAAAgh4QYAA2gu9SBsQQAABBBBAAAEE0iZAAJ02anaEAAIIIIAAAggg4AUB\nAmgv9CJtQAABBBBAAAEEEEibAAF02qjZEQIIIIAAAggggIAXBAigvdCLtAEBBBBAAAEEEEAg\nbQIE0GmjZkcIIIAAAggggAACXhAggPZCL9IGBBBAAAEEEEAAgbQJEECnjZodIYAAAggggAAC\nCHhBgADaC71IGxBAAAEEEEAAAQTSJkAAnTZqdoQAAggggAACCCDgBQECaC/0Im1AAAEEEEAA\nAQQQSJsAAXTaqNkRAggggAACCCCAgBcECKC90Iu0AQEEEEAAAQQQQCBtAv8P8GhahVS9zIYA\nAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 240,
       "width": 360
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 定义成功次数和研究总次数\n",
    "y <- 1  # 成功次数\n",
    "n <- 6  # 研究总次数\n",
    "\n",
    "# 计算似然值，对于三种不同的成功概率 p\n",
    "p_values <- c(0.5, 0.8, 0.2)  # 定义三种成功率\n",
    "likelihoods <- sapply(p_values, function(p) dbinom(y, size = n, prob = p))  # 计算似然值\n",
    "\n",
    "# 创建数据框存储结果\n",
    "data <- data.frame(p_values, likelihoods)\n",
    "\n",
    "# 创建图形\n",
    "options(repr.plot.width=6, repr.plot.height=4) #自定义画布大小                \n",
    "ggplot(data, aes(x = p_values, y = likelihoods)) +\n",
    "  geom_segment(aes(xend = p_values, yend = 0), color = \"gray\", size = 1) +  \n",
    "  geom_point(color = \"black\",size = 3) + \n",
    "  labs(y = 'f(y|π)', x = expression(pi)) +  # 设置坐标轴标签\n",
    "  xlim(0, 1) +\n",
    "  scale_y_continuous(expand = c(0,0),limits = c(0, 0.45)) +\n",
    "  APA_theme"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a79c2148",
   "metadata": {
    "_id": "72AC4CDC23224E4D922F9C883E946616",
    "id": "CA27669176924C0CA2E9F06C49C416DF",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "**似然函数**  \n",
    "\n",
    "当团队只成功复现一次时，该事件在不同成功率下出现的可能性可以写为：  \n",
    "\n",
    "$$  \n",
    "f(Y=1|\\pi=0.2) = \\binom{6}{1} 0.2^1 (1-0.2)^{5}  \n",
    "$$  \n",
    "$$  \n",
    "f(Y=1|\\pi=0.5) = \\binom{6}{1} 0.5^1 (1-0.5)^{5}  \n",
    "$$  \n",
    "$$  \n",
    "f(Y=1|\\pi=0.8) = \\binom{6}{1} 0.8^1 (1-0.8)^{5}  \n",
    "$$  \n",
    "\n",
    "因此，成功复现次数为1时的似然函数可以写成  \n",
    "\n",
    "$$  \n",
    "L(\\pi|y=1) = f(y=1|\\pi) = \\binom{6}{1} \\pi^{1}(1-\\pi)^{6-1} = 6\\pi(1-\\pi)^{5}  \n",
    "$$  \n",
    "\n",
    "不同成功率下的似然：  \n",
    "\n",
    "| $\\pi$          | 0.2   | 0.5   | 0.8   |  \n",
    "|---------------|-------|-------|-------|  \n",
    "| $L(\\pi \\| y=1)$ | 0.3932 | 0.0938 | 0.0015 |  \n",
    "\n",
    "\n",
    "\n",
    "\n",
    "**注意：**  \n",
    "\n",
    "似然函数表示的是，在各种可能的成功率$\\pi$下,成功次数$Y=1$的可能性，所以  \n",
    "1. 该似然函数公式只取决于$\\pi$  \n",
    "2. 似然函数的总和加起来不为1（从条件概率的公式来看，似然函数的分母是不同的）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22fc2537",
   "metadata": {
    "_id": "D0F1C949052B4862A5FF3F952B56246C",
    "id": "44277785C6124A7D8CC7F49DB1E35396",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "#### 条件概率 VS 似然函数  \n",
    "\n",
    "🤓  \n",
    "当$\\pi$是一定时，条件概率质量函数$f(·|\\pi)$可以帮我们计算在$\\pi$取值下（各种模型），不同的数据$Y$(e.g., $y_{1},y_{2}$)发生的可能性。  \n",
    "$$  \n",
    "f(y_{1}|\\pi) \\; vs \\; f(y_{2}|\\pi)  \n",
    "$$  \n",
    "\n",
    "当$Y = y$一定时，似然函数$L(·|y)= f(y|·)$允许我们比较在各种不同的模型，即二项式的$\\pi$取值(e.g., $\\pi_{1},\\pi_{2}$)下，观察到这个数据$y$的可能性(relative likelihood)。  \n",
    "\n",
    "\n",
    "$$  \n",
    "L(\\pi_{1}|y) \\; \\text{与} \\; L(\\pi_{2}|y)  \n",
    "$$  \n",
    "$$  \n",
    "\\text{即}  \n",
    "$$  \n",
    "$$  \n",
    "f(y|\\pi_{1}) \\; \\text{与} \\; f(y|\\pi_{2})  \n",
    "$$  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0091a815",
   "metadata": {
    "_id": "37CA7578F4774A4A80CE7B13B1DCFBE0",
    "id": "11A59BC5521C4320962FCEDCD9835765",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "**在二项分布模型下...**  \n",
    "\n",
    "进行$n = 6$个重复实验时，成功次数与成功率的关系符合二项式模型，可以用如下的形式来表示：  \n",
    "\n",
    "$$  \n",
    "Y|\\pi \\sim Bin(6,\\pi)  \n",
    "$$  \n",
    "\n",
    "\n",
    "$$  \n",
    "f(y|\\pi) = \\binom{6}{y} \\pi^{y}(1-\\pi)^{6-y} \\quad\\quad for\\;y \\in \\{0,1,2,3,4,5,6\\}  \n",
    "$$  \n",
    "\n",
    "-----------------------------------  \n",
    "\n",
    "下图给出了几种 $\\pi$的取值，我们可以通过概率模型得到每种$Y$发生的可能性。  \n",
    "* 同时，我们可以看到，Y=1(赢一次)这一特定的数据模式，在各个$\\pi$取值(模型)下的似然。  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0244e745-94bd-488d-adb7-8ee232172347",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WUz/lYkfK+5QA1nV6uaAIEOCjT8CNIx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\nAQIECBAgQIAAAQIEGiHw/wGn66DVbFMo6wAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 定义成功次数和总试验次数\n",
    "y <- 0:6  # 成功次数 (0到6)\n",
    "n <- 6    # 研究总次数\n",
    "pi_values <- c(0.2, 0.5, 0.8)  # 三种不同的成功概率\n",
    "\n",
    "# 创建一个空列表来存储每个概率的结果\n",
    "plots <- list()\n",
    "\n",
    "# 循环生成每个概率的图\n",
    "for (i in seq_along(pi_values)) {\n",
    "  pi <- pi_values[i]\n",
    "  # 计算似然值\n",
    "  likelihoods <- dbinom(y, size = n, prob = pi)\n",
    "  y_1 <- dbinom(1, size = 6, prob = pi)  \n",
    "\n",
    "  # 绘制图形\n",
    "  data <- data.frame(y = y, likelihoods = likelihoods)\n",
    "  y_label <- ifelse(i == 1, \"f(y|π)\", \"\")\n",
    "\n",
    "  p <- ggplot(data, aes(x = y, y = likelihoods)) +\n",
    "    geom_segment(aes(xend = y, yend = 0), color = \"black\") +\n",
    "    geom_segment(x = 1, y = 0, xend = 1, yend = y_1, color = \"black\", size = 1.5) +\n",
    "    geom_point(color = \"black\", size = 3) +\n",
    "    labs(\n",
    "      title = paste(\"Bin(\", n, \",\", pi, \")\", sep = \"\"),\n",
    "      x = \"y\",\n",
    "      y = y_label  \n",
    "    ) +\n",
    "    scale_y_continuous(expand = c(0, 0), limits = c(0, 0.5)) +\n",
    "    APA_theme\n",
    "  \n",
    "  plots[[as.character(pi)]] <- p\n",
    "}\n",
    "\n",
    "options(repr.plot.width = 12, repr.plot.height = 6)\n",
    "grid.arrange(grobs = plots, ncol = 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f893fd64",
   "metadata": {
    "_id": "45541A93BE7B4F15B21B9284010EE053",
    "id": "CEA95B2883354165B950F960D06CB637",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### 先验概率模型(**Prior** probability model)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3f79ae9",
   "metadata": {
    "_id": "8F39E31E1E4D40299FC0523F74F844E3",
    "id": "FAE5F28DE44446C4A399FEA40B7C8EDE",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "**建立先验模型**  \n",
    "\n",
    "从前面的描述可以看到，二项分布的参数$\\pi$也可以变化，也可以成为一个随机变量。  \n",
    "\n",
    "- 例如，我们想当一个更有深度的观察者，融合了乐观派、悲观派和中立者三者关于$\\pi$的估计。  \n",
    "- 但是，我们对三种观点的可能性有不同的信念。  \n",
    "\n",
    "假如我们总体上是一个乐观派，但不排除悲观派的观点，我们给三派观点分配了一定的概率(先验)。  \n",
    "- 例如，设定 $\\pi_{0.2} = 0.1$， 或者 $\\pi_{0.2} = 0.5$。 但需要所有$f(\\pi)$的总和为1。  \n",
    "\n",
    "\n",
    "| $\\pi$\t    |0.2  |0.5 |0.8 |Total  \n",
    "|---------- |-----|----|----|-----|  \n",
    "|$f(\\pi)$   |0.10  |0.25 |0.65   |1|  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5243b494",
   "metadata": {
    "_id": "C4F7FE361F3B4A6F9838D276D5CE8611",
    "id": "B552B6DCD27D4CBA955B5A3C454D03A9",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "我们设定的$\\pi$ 的数量也是可以变化的。  \n",
    "\n",
    "- 例如，我们还可以将一种非常悲观的可能性也纳入进来，认为该团队成功率为0.01，即 $\\pi = 0.01$。  \n",
    "- 那么新形成的先验分布可能如下。  \n",
    "\n",
    " \n",
    "| $\\pi$    |   0.01  | 0.2  | 0.5  | 0.8  | Total |  \n",
    "| -------- | --- | ---- | ---- | ---- | ----- |  \n",
    "| $f(\\pi)$ |  0.10   | 0.10 | 0.25 | 0.55 | 1     |  \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f6a12b6",
   "metadata": {
    "_id": "38E98221461549329E95D8DA03AD6D66",
    "id": "1C61EB98A68648C891934A6F50E534DF",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### 后验概率模型(Posterior probability model)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b01e8e8a",
   "metadata": {
    "_id": "64BEDA6DE1DD49E18C1669669168502C",
    "id": "3B67DC97ABE94D7E8B77894796FB3602",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "前述第一个先验模型，我们总体上是乐观的，认为团队高成功率的可能性很高 ($\\pi_{0.8} = 0.65$)。  \n",
    "\n",
    "\n",
    "\n",
    "| $\\pi$\t    |0.2  |0.5 |0.8 |Total  \n",
    "|---------- |-----|----|----|-----|  \n",
    "|$f(\\pi)$   |0.10  |0.25 |0.65   |1|  \n",
    "\n",
    "\n",
    "\n",
    "然而，最终结果发现：该团队只成功复现一次。  \n",
    "\n",
    "这个新的数据会如何改变我们的信念？"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1642503-7410-4c19-87c9-209da75dc2b2",
   "metadata": {},
   "source": [
    "我们可以综合先验和似然，根据贝叶斯的思路，计算后验概率。\n",
    "\n",
    "其中 团队成功复现的概率从降低为。意味着，他成功率为0.2的可能性是最大的 。\n",
    "\n",
    "左图为先验模型\n",
    "中间的图为似然模型\n",
    "右边的图为后验模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2af55a1e-1195-4c30-8176-5f76fcd84b2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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P2fVyFAgMCgArVD2JX+o1XuojvQdOlmTF/px7l83NquyzFcSilgK6+vnBhsqJrS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\n8CTJTQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Pi 值和对应的数据\n",
    "pi_values <- c(0.2, 0.5, 0.8)\n",
    "f_pi <- c(0.10, 0.25, 0.65)  # Prior probabilities\n",
    "L_pi_given_Y1 <- c(0.617, 0.367, 0.015)  # Likelihoods given Y=1\n",
    "posterior <- c(0.617, 0.367, 0.015)  # Posterior\n",
    "\n",
    "# 创建一个空列表来存储每个图的结果\n",
    "plots <- list()\n",
    "\n",
    "# 定义一个函数来绘制各个子图\n",
    "plot_function <- function(title, y_values) {\n",
    "  data <- data.frame(pi = pi_values, y = y_values)\n",
    "  \n",
    "  p <- ggplot(data, aes(x = pi, y = y)) +\n",
    "    geom_point(color = \"black\", size = 2) +  # 散点图\n",
    "    geom_segment(aes(xend = pi, yend = 0), color = \"black\", size = 1) +  # 垂直线\n",
    "    labs(title = title, x = expression(pi), y = \"Probability\") +  # 设置标题和标签\n",
    "    scale_y_continuous(expand = c(0, 0), limits = c(0, 0.7)) +  # 设置y轴范围\n",
    "    scale_x_continuous(expand = expansion(mult = c(0.1, 0.1))) +\n",
    "    APA_theme\n",
    "  return(p)\n",
    "}\n",
    "\n",
    "# 绘制先验概率\n",
    "plots[[1]] <- plot_function(\"Prior f(π)\", f_pi)\n",
    "# 绘制似然函数\n",
    "plots[[2]] <- plot_function(\"Likelihood L(π|Y=1)\", L_pi_given_Y1)\n",
    "# 绘制后验概率\n",
    "plots[[3]] <- plot_function(\"Posterior f(π|Y=1)\", posterior)\n",
    "\n",
    "# 使用 gridExtra 将各个子图放在一起\n",
    "options(repr.plot.width = 14, repr.plot.height = 5)\n",
    "grid.arrange(grobs = plots, ncol = 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c55794f9",
   "metadata": {
    "_id": "6E5372D39F5D48D58461B9A071A46D9C",
    "id": "99BD84BB6ED14F57B09254FE00FAE21D",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "**后验模型的计算过程**  \n",
    "\n",
    "上图所表示的后验可写成：  \n",
    "\n",
    "$$  \n",
    "f(\\pi|y=1)  \n",
    "$$  \n",
    "\n",
    "表示当团队只赢成功复现一项研究时，他成功率$\\pi$的概率分布  \n",
    "\n",
    "根据贝叶斯公式，我们可以进一步对后验概率公式进行展开：  \n",
    "\n",
    "$$  \n",
    "posterior = \\frac{ prior*likelihood} {normalizing\\;\\;constant}  \n",
    "$$  \n",
    "\n",
    "$$  \n",
    "f(\\pi|y=1) = \\frac{ f(\\pi)L(\\pi|y=1)} {f(y=1)} \\quad\\quad for\\;\\pi \\in {0.2,0.5,0.8}  \n",
    "$$  \n",
    "\n",
    "$$  \n",
    "f(\\pi=0.2|y=1) = \\frac{0.10 \\times 0.3932} {0.0637} \\approx 0.617  \n",
    "$$  \n",
    "$$  \n",
    "f(\\pi=0.5|y=1) = \\frac{0.25 \\times 0.0938} {0.0637} \\approx 0.368  \n",
    "$$  \n",
    "$$  \n",
    "f(\\pi=0.8|y=1) = \\frac{0.65 \\times 0.0015} {0.0637} \\approx 0.015  \n",
    "$$ \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c8a727b",
   "metadata": {
    "_id": "8436F519D4D24363BC40B88942193A50",
    "id": "EA407E43E22F46FBB36F3A6E8A9E9C60",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "下表对后验概率模型进行了总结，我们可知，经过了先前只成功了一项研究的复现经历后，该团队取得成功($\\pi$=0.8)的可能性已经从0.65降到了0.015  \n",
    "\n",
    "\n",
    "| $\\pi$\t        |0.2    |0.5    |0.8 |Total  \n",
    "|---------------|-----  |----   |----|-----|  \n",
    "|$f(\\pi)$   |0.10  |0.25 |0.65|1|  \n",
    "|$f(\\pi \\| y=1)$   |0.617  |0.368 |0.015|1|  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2ee55a5",
   "metadata": {
    "_id": "08F23756A40C45C19D184E7F115C95E0",
    "id": "98A72E08C66047AAAB79BCF043DDAE90",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "**补充材料**  \n",
    "\n",
    "省略分母的计算  \n",
    "- 在贝叶斯统计中，后验概率的计算公式是：\n",
    "\n",
    "$$\n",
    "P(\\pi|y) = \\frac{P(y|\\pi) \\cdot P(\\pi)}{P(y)} \\propto P(y|\\pi) \\cdot P(\\pi)\n",
    "$$\n",
    "\n",
    "- **$P(\\pi|y)$** 是后验概率。\n",
    "- **$P(y|\\pi)$** 是似然函数。\n",
    "- **$P(\\pi)$** 是先验概率。\n",
    "- 分母 **$P(y)=\\int P(y|\\pi) \\cdot P(\\pi) d \\theta$** 是边际似然。\n",
    "\n",
    "由于分母 **$P(y)$**（边际似然）在不同参数 **$\\pi$** 下是一个常数，因此在比较不同后验概率时，我们可以省略这个常数，因为它对所有的后验概率是相同的。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9daafd4",
   "metadata": {},
   "source": [
    "\n",
    "因此，虽然我们计算的值并不总和为 1，但它们的比例关系没有改变，仍然可以用于比较不同参数下的后验概率。这就是为什么我们可以只关注 **$P(y|\\pi) \\cdot P(\\pi)$** 而不需要计算完整的后验概率。\n",
    "\n",
    "那么既然$f(y)$是一个用来标准化的常数，它并不受$\\pi$的影响，那么后验概率质量函数$f(\\pi|y)$ 就与$f(\\pi)$和$L(\\pi|y)$成正比  \n",
    "\n",
    "$$  \n",
    "f(\\pi | y) = \\frac{f(\\pi)L(\\pi|y)}{f(y)} \\propto f(\\pi)L(\\pi|y)  \n",
    "$$  \n",
    "即，  \n",
    "\n",
    "$$  \n",
    "posterior \\propto prior⋅ likelihood  \n",
    "$$  \n",
    "\n",
    "省略分母后验的计算可写成：  \n",
    "$$  \n",
    "f(\\pi=0.2|y=1) \\propto 0.10⋅0.3932  =0.039320  \n",
    "$$  \n",
    "\n",
    "$$  \n",
    "f(\\pi=0.5|y=1) \\propto 0.25⋅0.0938 = 0.023450  \n",
    "$$  \n",
    "$$  \n",
    "f(\\pi=0.8|y=1) \\propto 0.65⋅0.0015 = 0.000975  \n",
    "$$  \n",
    "\n",
    "$\\propto$ 表示成比例，尽管这些未经标准化的后验概率总和不等于1  \n",
    "$$  \n",
    "0.039320 + 0.023450 + 0.000975 = 0.063745,  \n",
    "$$  \n",
    "但它们的比例关系并未改变(见下图)  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42135bc0",
   "metadata": {},
   "source": [
    "**Proportionality**  \n",
    "\n",
    "既然$f(y)$是一个用来标准化的常数，它并不受$\\pi$的影响，那么后验概率质量函数$f(\\pi|y)$ 就与$f(\\pi)$和$L(\\pi|y)$成正比  \n",
    "\n",
    "$$  \n",
    "f(\\pi | y) = \\frac{f(\\pi)L(\\pi|y)}{f(y)} \\propto f(\\pi)L(\\pi|y)  \n",
    "$$  \n",
    "即，  \n",
    "\n",
    "$$  \n",
    "posterior \\propto prior⋅ likelihood  \n",
    "$$  \n",
    "\n",
    "> 😜这个性质很重要。因为分母的计算量往往比较大，需要遍历所有参数，如果参数不止一个，计算量可想而知。因此，如过能不计算分母也能计算后验，那么这样的方法(后面会介绍的MCMC算法)将会非常有实践意义。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "8703d3a6",
   "metadata": {
    "_id": "E2DC4ED06D5D468495F62290EAE2A323",
    "collapsed": false,
    "id": "2E96EDB9D4F64E258E1620D7D81A0633",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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p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\nK/2hvc8nLWtj/NFSo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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 600
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Pi values and corresponding unnormalized posterior data\n",
    "pi_values <- c(0.2, 0.5, 0.8)\n",
    "unnormalized_posterior <- c(0.03932, 0.02345, 0.00097)  # Unnormalized posterior values\n",
    "normalized_posterior <- unnormalized_posterior / sum(unnormalized_posterior)  # Normalized\n",
    "\n",
    "# 创建数据框\n",
    "posterior_data <- data.frame(\n",
    "    pi = rep(pi_values, 2),\n",
    "    probability = c(normalized_posterior, unnormalized_posterior),\n",
    "    type = rep(c(\"normalized\", \"unnormalized\"), each = length(pi_values))\n",
    ")\n",
    "\n",
    "# 创建子图\n",
    "options(repr.plot.width=10, repr.plot.height=5) #自定义画布大小  \n",
    "ggplot(posterior_data, aes(x = pi, y = probability)) +\n",
    "    geom_segment(aes(xend = pi, yend = 0), color = \"black\", size = 1.5) +  # 绘制竖线\n",
    "    geom_point(color = \"black\", size = 3) +  # 绘制散点\n",
    "    facet_wrap(~type, scales = \"free_y\",labeller = labeller(type = c(normalized = \"Normalized\", unnormalized = \"Unnormalized\"),size=20)) +  # 创建子图\n",
    "    labs(x = expression(pi), y = \"Probability\") +  # 设置坐标轴标签\n",
    "    scale_y_continuous(expand = expansion(mult = c(0, 0.05))) +\n",
    "    scale_x_continuous(expand = expansion(mult = c(0.1, 0.1)))+\n",
    "    APA_theme +\n",
    "    theme(strip.text = element_text(size = 16))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd266b1d",
   "metadata": {
    "_id": "039AEF64DD0447A8AB7E4DD44248D1EF",
    "id": "E423D4DA6065413883F1D73C795C23D9",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "我们可以使用这些未经标准化的后验概率总和作为分母，来对后验概率进行标准化，会得到相同的计算结果。  \n",
    "\n",
    "$$  \n",
    "f(\\pi = 0.2 | y = 1) = \\frac{0.039320}{0.039320 + 0.023450 + 0.000975} \\approx 0.617  \n",
    "$$  \n",
    "\n",
    "注意，分母为所有似然值的总和，因此后验概率的计算公式还可以写成：  \n",
    "\n",
    "$$  \n",
    "f(\\pi | y) = \\frac{f(\\pi)L(\\pi|y)}{f(y)} = \\frac{f(\\pi)L(\\pi|y)}{\\sum_{\\text{all } \\pi} f(\\pi)L(\\pi|y)} .  \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40aac490",
   "metadata": {
    "_id": "F4A3D160AE5E4181A769E34E023A7033",
    "id": "EA2EB8F21DC54AF5A0AED9C66A000F39",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### Posterior simulation (with code)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a7fb330",
   "metadata": {
    "_id": "744BDB3097544121BB3C1C271A5EEEE0",
    "id": "115C8CB90FFC4BBB98035C8F8E4301C7",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### 1. 定义先验模型  \n",
    "- 定义多个可能的成功率  \n",
    "- 定义每个成功率出现的可能性 (注意，其和为1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "ebedef47",
   "metadata": {
    "_id": "AE14DA7DBF2E4C4AAC85A3A7A09A81B6",
    "collapsed": false,
    "id": "E68BBC4D52BA43FC9BBA149F645B5DA0",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# 定义可能的成功率\n",
    "replicated <- data.frame(pi = c(0.2, 0.5, 0.8))\n",
    "\n",
    "# 定义先验模型\n",
    "prior <- c(0.10, 0.25, 0.65)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c65dc3d9",
   "metadata": {
    "_id": "A5593998CBBE463084B2DB31E612BAEB",
    "id": "7AEDC92C0D58482DAE485896D4BB3845",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### 2. 模拟在特定成功率下，6项研究中的成功次数  \n",
    "- 重复这个过程10000次"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "11543b08",
   "metadata": {
    "_id": "EB13D3BBC8AA444EB4751606BAE3948F",
    "collapsed": false,
    "id": "AA582F8D251044BF9D8D1A8DD4FFCFBE",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  pi y\n",
      " 0.5 3\n",
      " 0.5 3\n",
      " 0.8 4\n",
      " 0.2 1\n",
      " 0.5 3\n",
      " 0.8 3\n",
      " 0.8 6\n",
      " 0.8 4\n",
      " 0.5 3\n",
      " 0.8 4\n"
     ]
    }
   ],
   "source": [
    "# 设置随机数种子保证可重复性\n",
    "set.seed(84735)\n",
    "\n",
    "# 从先验中抽取10000个\n",
    "replicated_sim_indices <- sample(1:nrow(replicated), size = 10000, replace = TRUE, prob = prior)\n",
    "replicated_sim <- replicated[replicated_sim_indices, , drop = FALSE]\n",
    "replicated_sim$y <- rbinom(n = nrow(replicated_sim), size = 6, prob = replicated_sim$pi)\n",
    "\n",
    "# 显示前10行数据\n",
    "print(head(replicated_sim, 10),row.names = FALSE)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "f1e89659",
   "metadata": {
    "_id": "178104DAE86849BE8666A37AA8AB472E",
    "collapsed": false,
    "id": "3897FD3D995F4A9E9A22E4DDD683964D",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[90m# A tibble: 3 × 3\u001b[39m\n",
      "     pi     n percentage\n",
      "  \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[90m<int>\u001b[39m\u001b[23m      \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m\n",
      "\u001b[90m1\u001b[39m   0.2  \u001b[4m1\u001b[24m017      0.102\n",
      "\u001b[90m2\u001b[39m   0.5  \u001b[4m2\u001b[24m521      0.252\n",
      "\u001b[90m3\u001b[39m   0.8  \u001b[4m6\u001b[24m462      0.646\n"
     ]
    }
   ],
   "source": [
    "# 对 pi 的抽取情况进行总结\n",
    "replicated_counts <- replicated_sim %>%\n",
    "  group_by(pi) %>%\n",
    "  summarise(n = n(), .groups = 'drop') %>%\n",
    "  mutate(percentage = n / sum(n)) %>%\n",
    "  arrange(pi)\n",
    "\n",
    "# 打印统计结果\n",
    "print(replicated_counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6315f6ab",
   "metadata": {
    "_id": "AD3A5819F20D461597DD4193AF4D8A37",
    "id": "69E4FCCFDB814FC394C8BA36278F111F",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### 3.  不同成功率下，不同成功次数的分布情况$f(y|\\pi)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "54dab2eb",
   "metadata": {
    "_id": "0F1BFF8B7EB74713A32B5E4C20A98CFA",
    "collapsed": false,
    "id": "2A2ADF4EAA834FF9A71D3F4819047CE9",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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991J0KgiwXKAwXlY6U0VLy+ffuG+AfJscceW5Il3ryfNm1a+hPHQ/rYxz4WkrcG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\nAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 300,
       "width": 840
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 创建三个分图\n",
    "plot_list <- lapply(c(0.2, 0.5, 0.8), function(pi_value) {\n",
    "  ggplot(replicated_sim[replicated_sim$pi == pi_value, ], aes(x = y, stat = \"count\")) +\n",
    "    geom_bar(aes(y = ..count.. / sum(..count..)), \n",
    "                   binwidth = 1, \n",
    "                   fill = \"skyblue\", color = \"black\") +  \n",
    "    labs(title = paste(\"Distribution of y for π =\", pi_value),\n",
    "         y = \"Probability\",\n",
    "         x = \"y\") +\n",
    "    scale_y_continuous(expand = expansion(mult = c(0, 0.05))) +\n",
    "    scale_x_continuous(expand = expansion(mult = c(0.1, 0.1)),limits = c(0,7))+\n",
    "    APA_theme\n",
    "})\n",
    "\n",
    "# 使用 gridExtra 将各个子图放在一起\n",
    "options(repr.plot.width=14, repr.plot.height=5) #自定义画布大小  \n",
    "grid.arrange(grobs = plot_list, ncol = 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2864ab44",
   "metadata": {
    "_id": "A9FFE801A1A24AEC97683A82E1DED0CF",
    "id": "327AE046C4E94B10A9E1913C37CC845C",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "### 4. 查看$y=1$时，对应的$\\pi$的分布情况"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "796db5cc",
   "metadata": {
    "_id": "B07F0C7DA92949F8B37A353DD13C21AC",
    "collapsed": false,
    "id": "5A432422434A4340A638852042F1DB65",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[90m# A tibble: 3 × 2\u001b[39m\n",
      "     pi     n\n",
      "  \u001b[3m\u001b[90m<dbl>\u001b[39m\u001b[23m \u001b[3m\u001b[90m<int>\u001b[39m\u001b[23m\n",
      "\u001b[90m1\u001b[39m   0.2   404\n",
      "\u001b[90m2\u001b[39m   0.5   253\n",
      "\u001b[90m3\u001b[39m   0.8    12\n"
     ]
    }
   ],
   "source": [
    "# 过滤出 y = 1 的情况\n",
    "replicated_post <- replicated_sim %>% filter(y == 1)\n",
    "# 对 pi 的抽取情况进行总结\n",
    "y_1_counts <- replicated_post %>%\n",
    "  group_by(pi) %>%\n",
    "  summarise(n = n(), .groups = 'drop') %>%\n",
    "  arrange(pi)\n",
    "\n",
    "# 打印统计结果\n",
    "print(y_1_counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "d63bca0f",
   "metadata": {
    "_id": "E05EE4EBAB694DA3998A35F52F1512D9",
    "collapsed": false,
    "id": "57BF0CF526A84C67A5A624D17DEAF1D4",
    "jupyter": {
     "outputs_hidden": false
    },
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZjMrv8vQaIt3/zmN9M555zT0sbh1N2tY+LvWYyoaC4xhL7572LzPssECBDoJYFx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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 480
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 使用 ggplot 绘制 y = 1 时 pi 的分布图\n",
    "options(repr.plot.width=8, repr.plot.height=6) #自定义画布大小  \n",
    "ggplot(replicated_post, aes(x = pi)) +\n",
    "  geom_histogram(aes(y = ..count.. ), binwidth = 0.1, fill = \"darkblue\", alpha = 0.7) +\n",
    "  scale_x_continuous(breaks = c(0.2, 0.5, 0.8)) +\n",
    "  labs(title = \"Distribution of π when y = 1\",\n",
    "       x = expression(pi),\n",
    "       y = \"counts\") +\n",
    "    scale_y_continuous(expand = expansion(mult = c(0, 0.05))) +\n",
    "  APA_theme"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1866f7e5",
   "metadata": {
    "id": "0A83B87D55634BE9AE6B3F2F73593ABA",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "思考：频率学派(经典统计)会如何处理上述两个问题？  \n",
    "* 某项研究的可重复性  \n",
    "* 重复6次的成功率"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61ede015",
   "metadata": {
    "_id": "CA3B0BC65DD34D54AE5114F0CE22A127",
    "id": "E209C1087EC14867ADE7F8E0718A9EE7",
    "jupyter": {},
    "notebookId": "66ea2e9f925f3bb1a291ea6b",
    "runtime": {
     "execution_status": null,
     "is_visible": false,
     "status": "default"
    },
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   "source": [
    "## Part 4: 频率学派与贝叶斯学派的对比"
   ]
  },
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   "source": [
    "最近的一篇综述讨论了贝叶斯方法在临床研究设计和分析中的应用，同时比较了贝叶斯与频率主义方法之间的哲学和方法论差异。  \n",
    "\n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/sjzj8nd4te.png?imageView2/0/w/640/h/640)  \n",
    "\n",
    "\n",
    "论文中展示的一个例子是一项用于治疗严重急性呼吸窘迫综合征（ARDS）的体外膜肺氧合法（ECMO）试验，研究体外膜肺氧合法（ECMO）对严重急性呼吸窘迫综合征（ARDS）的效果。该试验的结果引发了频率学派和贝叶斯学派在同一数据下得出不同结论的讨论。  \n",
    "\n",
    "> Goligher, E. C., Heath, A., & Harhay, M. O. (2024). Bayesian statistics for clinical research. The Lancet, 404(10457), 1067-1076."
   ]
  },
  {
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   "source": [
    "- 频率学派：试验原本计划招募331名患者，但因中期分析未能证明ECMO治疗具有显著益处，最终只招募了249名患者。结果显示，干预组的死亡率为35%，对照组为46%，表面上看治疗效果显著。然而，基于频率学派的统计分析，P值为0.09，并未达到通常的显著性水平（$p$<0.05）。  \n",
    "- 因此研究者得出结论：试验未能提供充分证据证明早期ECMO可以显著降低死亡率。"
   ]
  },
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    "- 贝叶斯学派：通过使用不同的先验分布时，H<sub>1</sub>（ECMO可以有效降低干预组死亡率）成立的后验概率在88%至99%之间。  \n",
    "- 这意味着，贝叶斯方法提供了强有力的证据支持ECMO的效果，甚至有学者建议，ECMO方法应被认为是一种有效的治疗手段。"
   ]
  },
  {
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   "source": [
    "### 频率学派如何看待这个世界？  \n"
   ]
  },
  {
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   "source": [
    "在对比频率学派与贝叶斯学派的差异之前，让我们首先回顾一下频率学派是如何看待这个世界的。"
   ]
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   "source": [
    "值得注意的是：  \n",
    "\n",
    "1. 固定的假设：频率学派认为假设（通常是零假设）是一个固定的命题。例如，在试验中，频率学派的零假设是“ECMO对死亡率没有显著影响”。  \n",
    "\n",
    "2. 数据的随机性：在频率学派的框架下，数据被视为随机变量。通过对这些数据进行分析，频率学派关注在假设为真的前提下，观测到当前数据或更极端数据的概率，即$p$值。  \n",
    "\n",
    "3. 无限重复实验的假设：频率学派的推断依赖于假设实验可以无限重复进行，进而通过计算在这些重复实验中得到观测数据的频率来推断真相。因此，置信区间也是基于多次实验的频率分布。  \n",
    "\n",
    "4. 拒绝或接受零假设：通过计算$p$值，频率学派根据预设的显著性水平（通常为0.05）决定是否拒绝零假设。"
   ]
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    "最后，频率学派如何**推断**出两个总体之间的差异？   \n",
    "- 频率学派通过零假设的显著性检验(Null hypothesis significant test, NHST)来判断显著性。通过计算置信区间(confidence interval)和$p$值来帮助推断过程。  \n",
    "- 在该临床试验中，通过$p$值（如，0.09）和置信区间来推断两个总体之间的差异。"
   ]
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   "source": [
    "### 贝叶斯学派如何看待这个世界？"
   ]
  },
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    "与频率学派不同，贝叶斯学派认为，概率是对不确定性的主观度量。  \n",
    "贝叶斯学派的核心思想包括：  \n",
    "1. 先验概率：贝叶斯学派从研究者对某个假设的初始信念（即先验概率）出发。这一信念可以基于以往研究、专家意见或临床经验。  \n",
    "2. 更新信念：当新数据（如试验结果）出现时，贝叶斯定理提供了一个框架，将先验概率与新证据（通过似然函数表示）结合，生成后验概率。后验概率代表更新后的信念，即在观察到新数据后，某假设为真的概率。  \n",
    "3. 后验分布与可信区间(credible intervals)：通过后验概率，贝叶斯方法能够直接评估一个假设为真的可能性。例如，贝叶斯分析可以直接得出H<sub>1</sub>成立的后验概率（如88%）。可信区间的概念也更具直观性，它表示在现有数据和先验信息下，某参数位于该区间内的概率。"
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   "source": [
    "#### Thomas Bayes  \n",
    "![Image Name](https://pic2.zhimg.com/v2-ae48785e2b67af851e236b3d38c78c8d_r.jpg)  \n"
   ]
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    "#### Pierre Simon Laplace  \n",
    "\n",
    "![Image Name](https://th.bing.com/th/id/R.c252b05834293b10a3005882940d6622?rik=Kr8G5HIK%2fObbHw&riu=http%3a%2f%2fimages.fineartamerica.com%2fimages-medium-large%2fpierre-simon-marquis-de-laplace-maria-platt-evans.jpg&ehk=uHIIZ0qdCLmD0FXAHR4lUGfySQGNKlhNkJgoWIOMJG4%3d&risl=&pid=ImgRaw&r=0)  \n"
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   "source": [
    "### 两个学派的差异对比  \n",
    "\n",
    "| **频率学派**                                           | **贝叶斯学派**                                         |  \n",
    "|-------------------------------------------------------|-------------------------------------------------------|  \n",
    "| **概率定义**：概率是事件在无限重复试验中的频率          | **概率定义**：概率是对假设的信念度量                   |  \n",
    "| **假设**：假设是固定的，数据是随机的                    | **假设**：假设是随机的，数据是固定的                   |  \n",
    "| **推断方式**：基于假设检验，通过$p$值判断是否拒绝零假设    | **推断方式**：通过更新先验与新数据计算后验概率         |  \n",
    "| **置信区间**：在重复试验中，95%的区间包含真实参数         | **可信区间**：给出某参数位于区间内的概率（如95%可信度） |  \n",
    "| **$p$值**：衡量在零假设下，观测数据或更极端数据的概率      | **后验概率**：给出假设为真的更新概率                   |  \n",
    "| **数据独立性**：推断只基于当前试验数据，不考虑先验信息    | **先验信息**：结合历史数据或专家意见，用于更新推断     |  \n",
    "| **实验重复性假设**：推断基于实验的假想重复性              | **逐步积累信息**：通过结合新数据不断更新和完善假设     |  \n",
    "| **适应性**：实验设计固定，不能在中途更新或调整             | **适应性**：可以灵活调整试验设计和决策，如自适应试验   |  \n",
    "\n",
    "来源：  \n",
    "> Goligher, E. C., Heath, A., & Harhay, M. O. (2024). Bayesian statistics for clinical research. The Lancet, 404(10457), 1067-1076."
   ]
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   "source": [
    "### 贝叶斯的主观性  \n",
    "\n",
    "**任何统计分析方法都不可能完全客观，因此主观性是一个相对概念:**  \n",
    "\n",
    "* 贝叶斯学派的主观性通过先验的设定来体现，透明，不易让人产生误解  \n",
    "\n",
    "* 频率学派的主观性暗含在各种**前提预设**中，比如方差分析中的方差齐性和正态性，这种看似‘客观的’预设，一方面难以满足，一方面也是一种主观的设定。  \n",
    "\n",
    "* 更为宏观的来说，样本的抽取，数据清理方式的选择，分析方法的选择，$p$值的设定，这些都存在主观性。因此，频率学派并没有想象的那么‘客观’。  \n",
    "\n",
    "* 主观不一定是坏事：通过量化方法将个体的经验和专家知识整合到数据分析之中。  \n",
    "\n"
   ]
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   "source": [
    "#### 重复抽样的不同作用"
   ]
  },
  {
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   "metadata": {
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   "source": [
    "##### 频率学派  \n",
    "* 统计推断依赖于参数的**抽样分布**，即只要无限(long-run)的进行抽样，样本分布的参数就会有某种分布形式；  \n",
    "* 零假设检验（Null Hypothesis Significance Testing，NHST）中的$p$值和置信区间的解读均依赖于“无限次抽样”的预设；  \n",
    "* 实际操作中，我们往往只会收集一次数据，并不会反复的进行抽样；有些情境中，预设“无限次重复抽样并不合理；  \n",
    "\n",
    "##### 贝叶斯学派  \n",
    "* 假定参数本身是分布，不确定性一起存在于推断之中；  \n",
    "* 直接根据数据对先验信念进行更新；  \n",
    "\n",
    "**置信区间(confidence intervals) vs 可信区间(credible intervals)**  \n",
    "\n",
    "**No free lunch: 各有优势和缺陷**"
   ]
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   "source": [
    "#### 不同的先验和似然会产生不同的后验分布  \n",
    "\n",
    "![Image Name](https://cdn.kesci.com/upload/image/rhqcb9gji7.png?imageView2/0/w/500/h/500)  \n"
   ]
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   "source": [
    "#### NHST的\"弱项\""
   ]
  },
  {
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   "metadata": {
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   "source": [
    "* 无法直接对零假设(null hypothesis)进行支持，即如果两个总体没有显著差异，他们的相似程度有多少？  (许岳培等, 2023, *应用心理学(04)*, 369-384)  \n",
    "\n",
    "* 一次性只能对比两个总体的假设进行比较；  \n",
    "\n",
    "* 控制假阳性是一个棘手的问题"
   ]
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  {
   "cell_type": "markdown",
   "id": "2e42d8be-8f49-4216-bf2d-299efde9ff16",
   "metadata": {},
   "source": [
    "# 附录  \n",
    "## 本节课python代码  \n",
    "\n",
    "注意：Python代码需要在python环境中运行，并且需要安装相关的包。和鲸平台中的`pyBayesian`这一计算环境为本课程2024年使用的python环境，包括了可运行的全部的python模块。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "63fc5b8d-9087-4541-a1b2-248b690711ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 导入数据加载和处理包：pandas\n",
    "import pandas as pd\n",
    "# 导入数字和向量处理包：numpy\n",
    "import numpy as np\n",
    "# 导入基本绘图工具：matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 使用 pandas 导入示例数据\n",
    "try:\n",
    "  df = pd.read_csv(\"/home/mw/input/bayes3797/replicated_language_cleaned.csv\") \n",
    "except:\n",
    "  df= pd.read_csv('data/replicated_language_cleaned.csv')\n",
    "\n",
    "df = df.drop('study_name', axis=1)\n",
    "df.head()\n",
    "\n",
    "# 设置APA 7的画图样式\n",
    "plt.rcParams.update({\n",
    "    'figure.figsize': (4, 3),      # 设置画布大小\n",
    "    'font.size': 12,               # 设置字体大小\n",
    "    'axes.titlesize': 12,          # 标题字体大小\n",
    "    'axes.labelsize': 12,          # 轴标签字体大小\n",
    "    'xtick.labelsize': 12,         # x轴刻度字体大小\n",
    "    'ytick.labelsize': 12,         # y轴刻度字体大小\n",
    "    'lines.linewidth': 1,          # 线宽\n",
    "    'axes.linewidth': 1,           # 轴线宽度\n",
    "    'axes.edgecolor': 'black',     # 设置轴线颜色为黑色\n",
    "    'axes.facecolor': 'white',     # 轴背景颜色（白色）\n",
    "    'xtick.direction': 'in',       # x轴刻度线向内\n",
    "    'ytick.direction': 'out',      # y轴刻度线向内和向外\n",
    "    'xtick.major.size': 6,         # x轴主刻度线长度\n",
    "    'ytick.major.size': 6,         # y轴主刻度线长度\n",
    "    'xtick.minor.size': 4,         # x轴次刻度线长度（如果启用次刻度线）\n",
    "    'ytick.minor.size': 4,         # y轴次刻度线长度（如果启用次刻度线）\n",
    "    'xtick.major.width': 1,        # x轴主刻度线宽度\n",
    "    'ytick.major.width': 1,        # y轴主刻度线宽度\n",
    "    'xtick.minor.width': 0.5,      # x轴次刻度线宽度（如果启用次刻度线）\n",
    "    'ytick.minor.width': 0.5,      # y轴次刻度线宽度（如果启用次刻度线）\n",
    "    'ytick.labelleft': True,       # y轴标签左侧显示\n",
    "    'ytick.labelright': False      # 禁用y轴标签右侧显示\n",
    "})\n",
    "\n",
    "df.head()\n",
    "\n",
    "# 数据预处理\n",
    "# 计算 'certain' 列的中位数\n",
    "median_certain = df['certain'].median()\n",
    "\n",
    "# 创建新列，编码规则：大于中位数为 1，小于等于中位数为 2\n",
    "df['language_style'] = df['certain'].apply(lambda x: 1 if x > median_certain else 0)\n",
    "\n",
    "# 输出结果\n",
    "df.head()\n",
    "\n",
    "# 计算不同水平的数量和百分比\n",
    "level_counts = df['replicated'].value_counts()\n",
    "level_percentages = df['replicated'].value_counts(normalize=True) * 100\n",
    "\n",
    "# 百分比保留两位小数\n",
    "level_percentages = level_percentages.round(2)\n",
    "\n",
    "# 创建一个新的 DataFrame 合并结果\n",
    "result_df1 = pd.DataFrame({'数量': level_counts, '百分比': level_percentages})\n",
    "# 展示结果(0代表不可重复，1代表可重复)\n",
    "result_df1\n",
    "\n",
    "# 计算不同水平的数量\n",
    "result_df2 = df.groupby(['replicated', 'language_style']).size().unstack()\n",
    "# 结果\n",
    "result_df2\n",
    "# 定义文章类型\n",
    "article = pd.DataFrame({'replicated': ['yes', 'no']})\n",
    "\n",
    "# 定义先验概率\n",
    "prior = [0.4, 0.6]\n",
    "\n",
    "# 模拟生成 10000 项研究，包括其类型\n",
    "np.random.seed(84735)\n",
    "article_sim = article.sample(n=10000, weights=prior, replace=True)\n",
    "# 查看前 10 行数据\n",
    "article_sim.head(10)\n",
    "\n",
    "#我们可以通过画图来查看这些被投放研究的可重复性比例。\n",
    "article_sim['replicated'].value_counts().plot.bar()\n",
    "plt.xticks(rotation=0)\n",
    "plt.show()\n",
    "\n",
    "# 设置条件概率\n",
    "article_sim['data_model'] = np.where(article_sim['replicated'] == 'no', 0.45, 0.56)\n",
    "\n",
    "# 定义研究是否使用确切语言\n",
    "data = ['certain', 'uncertain']\n",
    "\n",
    "# 设置随机种子，以便得到重复的结果\n",
    "rng=np.random.default_rng(84735)\n",
    "# 生成确切语言相关的数据\n",
    "article_sim['language'] = article_sim.apply(lambda x: rng.choice(data, 1, p = [x.data_model, 1-x.data_model])[0], axis=1)\n",
    "\n",
    "# 显示每个类别研究数量\n",
    "(\n",
    "  article_sim.groupby(['language', 'replicated'])\n",
    "    .size()\n",
    "    .unstack(fill_value=0)\n",
    ")\n",
    "\n",
    "usage_yes = article_sim[article_sim['language'] == 'certain']\n",
    "print('使用确切语言的研究', usage_yes['replicated'].value_counts().sum())\n",
    "usage_yes['replicated'].value_counts()\n",
    "\n",
    "# 定义两幅图的坐标\n",
    "fig, axes = plt.subplots(1, 2, figsize=(10, 5))\n",
    "\n",
    "# 绘制两幅图\n",
    "for i, u in enumerate(article_sim['language'].unique()):\n",
    "    ax = axes[i]\n",
    "    data = article_sim[article_sim['language'] == u]\n",
    "    ax.bar(data['replicated'].unique(), data['replicated'].value_counts())\n",
    "    ax.set_title(f'language = {u}')\n",
    "    ax.set_ylim(0, 10000) \n",
    "\n",
    "# 显示   \n",
    "fig.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# 导入数据加载和处理包：pandas\n",
    "import pandas as pd\n",
    "# 导入数字和向量处理包：numpy\n",
    "import numpy as np\n",
    "# 导入基本绘图工具：matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "# 导入高级绘图工具 seaborn 为 sns\n",
    "import seaborn as sns\n",
    "# 导入统计建模工具包 scipy.stats 为 st\n",
    "import scipy.stats as st \n",
    "\n",
    "# 设置APA 7的画图样式\n",
    "plt.rcParams.update({\n",
    "    'figure.figsize': (4, 3),      # 设置画布大小\n",
    "    'font.size': 12,               # 设置字体大小\n",
    "    'axes.titlesize': 12,          # 标题字体大小\n",
    "    'axes.labelsize': 12,          # 轴标签字体大小\n",
    "    'xtick.labelsize': 12,         # x轴刻度字体大小\n",
    "    'ytick.labelsize': 12,         # y轴刻度字体大小\n",
    "    'lines.linewidth': 1,          # 线宽\n",
    "    'axes.linewidth': 1,           # 轴线宽度\n",
    "    'axes.edgecolor': 'black',     # 设置轴线颜色为黑色\n",
    "    'axes.facecolor': 'white',     # 轴背景颜色（白色）\n",
    "    'xtick.direction': 'in',       # x轴刻度线向内\n",
    "    'ytick.direction': 'out',      # y轴刻度线向内和向外\n",
    "    'xtick.major.size': 6,         # x轴主刻度线长度\n",
    "    'ytick.major.size': 6,         # y轴主刻度线长度\n",
    "    'xtick.minor.size': 4,         # x轴次刻度线长度（如果启用次刻度线）\n",
    "    'ytick.minor.size': 4,         # y轴次刻度线长度（如果启用次刻度线）\n",
    "    'xtick.major.width': 1,        # x轴主刻度线宽度\n",
    "    'ytick.major.width': 1,        # y轴主刻度线宽度\n",
    "    'xtick.minor.width': 0.5,      # x轴次刻度线宽度（如果启用次刻度线）\n",
    "    'ytick.minor.width': 0.5,      # y轴次刻度线宽度（如果启用次刻度线）\n",
    "    'ytick.labelleft': True,       # y轴标签左侧显示\n",
    "    'ytick.labelright': False      # 禁用y轴标签右侧显示\n",
    "})\n",
    "\n",
    "y = [0,1,2,3,4,5,6]  # 成功次数 \n",
    "n = 6                # 重复研究总次数\n",
    "p = 0.5              # 假设的成功概率\n",
    "\n",
    "# 计算概率值\n",
    "prob = st.binom.pmf(y, n, p)\n",
    "\n",
    "result_table = pd.DataFrame({\"成功次数\":y, \"概率\":prob})\n",
    "result_table\n",
    "\n",
    "# 绘制灰色竖线\n",
    "for i, j in zip(y , prob):\n",
    "    plt.plot([i, i], [j, 0], 'gray', linestyle='-', linewidth=1, zorder=1, )\n",
    "\n",
    "# 绘制黑色点(各成功率次数的成功率)\n",
    "plt.scatter(y, prob, c='black')\n",
    "\n",
    "plt.ylabel('$f(y|\\pi)$')\n",
    "plt.xlabel('y')\n",
    "\n",
    "plt.xlim(-0.2,6.2)\n",
    "plt.ylim(0,0.5)\n",
    "plt.show()\n",
    "\n",
    "sum(result_table['概率'])\n",
    "\n",
    "y = [0,1,2,3,4,5,6]  # 成功次数 \n",
    "n = 6                # 研究总次数\n",
    "\n",
    "# 计算似然值\n",
    "p = 0.5              # 本团队假设的成功复现概率\n",
    "likelihood1 = st.binom.pmf(y, n, p)\n",
    "p = 0.8              # 乐观派的成功概率\n",
    "likelihood2 = st.binom.pmf(y, n, p)\n",
    "p = 0.2              # 悲观派眼中的成功概率\n",
    "likelihood3 = st.binom.pmf(y, n, p)\n",
    "\n",
    "result_table = pd.DataFrame({\n",
    "  \"成功次数\":y, \n",
    "  \"本团队(pi=0.5)\":likelihood1, \n",
    "  \"悲观派(pi=0.2)\":likelihood2, \n",
    "  \"乐观派(pi=0.8)\":likelihood3})\n",
    "result_table\n",
    "\n",
    "# 创建子图\n",
    "fig, axs = plt.subplots(1, 3, figsize=(10, 4))\n",
    "\n",
    "# 绘制三个图,每个子图类似原图\n",
    "three_pi = [\"Team itself ($\\pi = 0.5$)\",\"Optimists ($\\pi = 0.8$)\",\"Pessimists ($\\pi = 0.2$)\"]\n",
    "likelihoods = [likelihood1, likelihood2, likelihood3]\n",
    "for i, ax in enumerate(axs):\n",
    "    \n",
    "    ax.scatter(y, likelihoods[i], c='black')\n",
    "    \n",
    "    for xx, yy in zip(y, likelihoods[i]):\n",
    "        ax.plot([xx, xx], [yy, 0], 'gray', linestyle='-', linewidth=1, zorder=1)\n",
    "    \n",
    "    # 添加facet\n",
    "    ax.set_title(three_pi[i])\n",
    "\n",
    "    ax.set_xlim(-0.2,6.2)\n",
    "    ax.set_ylim(0,0.4)\n",
    "\n",
    "fig.supylabel('$f(y|\\pi)$')\n",
    "fig.supxlabel('y')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# 定义成功次数和研究总次数\n",
    "y = 1  # 成功次数，作为数组处理以便向量化计算\n",
    "n = 6  # 研究总次数\n",
    "\n",
    "# 计算似然值，对于三种不同的成功概率 p\n",
    "p_values = [0.5, 0.8, 0.2]          # 定义三种成功率\n",
    "likelihoods = []                    # 用于存储每种成功率的似然值结果\n",
    "\n",
    "for p in p_values:\n",
    "    likelihood = st.binom.pmf(y, n, p)  # 使用st.binom.pmf计算似然值\n",
    "    likelihoods.append(likelihood)      \n",
    "\n",
    "\n",
    "# 创建图形和子图\n",
    "fig, ax = plt.subplots()  \n",
    "ax.scatter(p_values, likelihoods, c='black')\n",
    "# 设置x轴和y轴的限制应该在绘制线条之前完成，以避免重复设置\n",
    "ax.set_xlim(-0.2, 1.2)  # x轴范围根据p_values调整，最大不应超过1\n",
    "ax.set_ylim(0, 0.5)\n",
    "for xx, yy in zip(p_values, likelihoods):\n",
    "    ax.plot([xx, xx], [0, yy], 'gray', linestyle='-', linewidth=1, zorder=1)\n",
    "    # 注意这里的顺序是 [0, yy] 而不是 [yy, 0]，因为我们希望从x轴画到对应的似然值\n",
    "# 设置坐标轴标签，直接使用ax的方法，而不是fig的方法\n",
    "ax.set_ylabel('$f(\\pi|y)$')  \n",
    "ax.set_xlabel('$\\pi$')       \n",
    "plt.tight_layout()  # 调整布局以避免标签重叠\n",
    "plt.show()\n",
    "\n",
    "# Values for Y (number of successes in n trials)\n",
    "y = np.arange(0, 7)\n",
    "# Number of trials (n) and different probabilities (π values)\n",
    "n = 6\n",
    "pi_values = [0.2, 0.5, 0.8]\n",
    "\n",
    "# Create subplots\n",
    "fig, axs = plt.subplots(1, 3, figsize=(12, 5))\n",
    "# Loop over each pi value to plot the corresponding binomial distribution\n",
    "for i, pi in enumerate(pi_values):\n",
    "    # Calculate binomial probabilities for each y (number of successes)\n",
    "    likelihoods = st.binom.pmf(y, n, pi)\n",
    "    \n",
    "    # Scatter plot of the likelihoods\n",
    "    axs[i].scatter(y, likelihoods, color='black', zorder=2)\n",
    "    \n",
    "    # Draw gray vertical lines\n",
    "    for yy, likelihood in zip(y, likelihoods):\n",
    "        axs[i].plot([yy, yy], [0, likelihood], color='gray', linestyle='-', linewidth=1, zorder=1)\n",
    "    \n",
    "    # Highlight y = 1 with a black line\n",
    "    axs[i].plot([1, 1], [0, st.binom.pmf(1, n, pi)], color='black', linewidth=3, zorder=3)\n",
    "    \n",
    "    # Title with binomial parameters\n",
    "    axs[i].set_title(f'Bin({n},{pi})')\n",
    "    \n",
    "    # Set y and x axis limits\n",
    "    axs[i].set_xlim(-0.5, 6.5)\n",
    "    axs[i].set_ylim(0, 0.5)\n",
    "\n",
    "# Global labels\n",
    "fig.supylabel(r'$f(y|\\pi)$')\n",
    "fig.supxlabel('y')\n",
    "\n",
    "# Adjust layout for better fit\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "本项目来源于和鲸社区，使用转载需要标注来源\n",
    "作者: ss\n",
    "来源: https://www.heywhale.com/mw/project/66e2c44e20251d33770337b6\n",
    "# Pi values and corresponding data\n",
    "pi_values = [0.2, 0.5, 0.8]\n",
    "f_pi = [0.10, 0.25, 0.65]  # Prior probabilities\n",
    "L_pi_given_Y1 = [0.617, 0.367, 0.015]  # Likelihoods given Y=1\n",
    "posterior = [0.617, 0.367, 0.015]  # Posterior, assumed same as likelihoods here\n",
    "\n",
    "# Create subplots for prior, likelihood, and posterior\n",
    "fig, axs = plt.subplots(1, 3, figsize=(10, 4))\n",
    "\n",
    "# Prior Probability f(π)\n",
    "axs[0].scatter(pi_values, f_pi, color='black', zorder=2)\n",
    "for xx, yy in zip(pi_values, f_pi):\n",
    "    axs[0].plot([xx, xx], [0, yy], color='black', linewidth=3, zorder=1)\n",
    "axs[0].set_title(r'Prior $f(\\pi)$')\n",
    "axs[0].set_xlim(0.15, 0.85)\n",
    "axs[0].set_ylim(0, 0.7)\n",
    "\n",
    "# Likelihood L(π|Y=1)\n",
    "axs[1].scatter(pi_values, L_pi_given_Y1, color='black', zorder=2)\n",
    "for xx, yy in zip(pi_values, L_pi_given_Y1):\n",
    "    axs[1].plot([xx, xx], [0, yy], color='black', linewidth=3, zorder=1)\n",
    "axs[1].set_title(r'Likelihood $L(\\pi|Y=1)$')\n",
    "axs[1].set_xlim(0.15, 0.85)\n",
    "axs[1].set_ylim(0, 0.7)\n",
    "\n",
    "# Posterior Probability f(π|Y=1)\n",
    "axs[2].scatter(pi_values, posterior, color='black', zorder=2)\n",
    "for xx, yy in zip(pi_values, posterior):\n",
    "    axs[2].plot([xx, xx], [0, yy], color='black', linewidth=3, zorder=1)\n",
    "axs[2].set_title(r'Posterior $f(\\pi|Y=1)$')\n",
    "axs[2].set_xlim(0.15, 0.85)\n",
    "axs[2].set_ylim(0, 0.7)\n",
    "\n",
    "# Set labels and layout\n",
    "for ax in axs:\n",
    "    ax.set_xlabel(r'$\\pi$')\n",
    "\n",
    "fig.supylabel('Probability')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Pi values and corresponding unnormalized posterior data\n",
    "pi_values = [0.2, 0.5, 0.8]\n",
    "unnormalized_posterior = [0.03932, 0.02345, 0.00097]  # Unnormalized posterior values\n",
    "normalized_posterior = [val / sum(unnormalized_posterior) for val in unnormalized_posterior]  # Normalized\n",
    "\n",
    "# Create subplots for normalized and unnormalized posteriors\n",
    "fig, axs = plt.subplots(1, 2, figsize=(8, 4))\n",
    "\n",
    "# Normalized posterior\n",
    "axs[0].scatter(pi_values, normalized_posterior, color='black', zorder=2)\n",
    "for xx, yy in zip(pi_values, normalized_posterior):\n",
    "    axs[0].plot([xx, xx], [0, yy], color='black', linewidth=3, zorder=1)\n",
    "axs[0].set_title('Normalized $f(\\pi | y=1)$')\n",
    "axs[0].set_xlim(0.15, 0.85)\n",
    "axs[0].set_ylim(0, 0.7)\n",
    "\n",
    "# Unnormalized posterior\n",
    "axs[1].scatter(pi_values, unnormalized_posterior, color='black', zorder=2)\n",
    "for xx, yy in zip(pi_values, unnormalized_posterior):\n",
    "    axs[1].plot([xx, xx], [0, yy], color='black', linewidth=3, zorder=1)\n",
    "axs[1].set_title('Unnormalized $f(\\pi | y=1)$')\n",
    "axs[1].set_xlim(0.15, 0.85)\n",
    "axs[1].set_ylim(0, 0.05)\n",
    "\n",
    "# Set labels and layout\n",
    "for ax in axs:\n",
    "    ax.set_xlabel(r'$\\pi$')\n",
    "\n",
    "fig.supylabel('Probability')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# 定义可能的成功率\n",
    "replicated = pd.DataFrame({'pi':[0.2, 0.5, 0.8]})\n",
    "\n",
    "# 定义先验模型\n",
    "prior = [0.10, 0.25, 0.65]\n",
    "\n",
    "# 设置随机数种子保证可重复性\n",
    "np.random.seed(84735)\n",
    "\n",
    "# 从先验中抽取10000个 pi 值，并生成对应的y值\n",
    "\n",
    "replicated_sim = replicated.sample(n=10000, weights=prior, replace=True)\n",
    "replicated_sim['y'] = np.random.binomial(n=6, p=replicated_sim['pi'], size=len(replicated_sim))\n",
    "replicated_sim.head(10)\n",
    "\n",
    "#对pi的抽取情况进行总结\n",
    "replicated_counts =  replicated_sim['pi'].value_counts().reset_index()\n",
    "\n",
    "replicated_counts.columns = ['pi','n']\n",
    "\n",
    "replicated_counts['percentage'] = (replicated_counts['n']/len(replicated_sim))\n",
    "\n",
    "replicated_counts = replicated_counts.sort_values(by='pi')\n",
    "\n",
    "print(replicated_counts)\n",
    "\n",
    "# 导入绘图工具 seaborn\n",
    "import seaborn as sns\n",
    "# 通过 facegrid 方法根据不同变量绘制不同的图形\n",
    "replicated_lik = sns.FacetGrid(replicated_sim,col=\"pi\")\n",
    "replicated_lik.map(sns.histplot,'y',stat='probability',discrete=True)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "replicated_post = replicated_sim[replicated_sim['y'] == 1].value_counts()\n",
    "replicated_post\n",
    "\n",
    "replicated_post = replicated_sim[replicated_sim['y'] == 1]\n",
    "\n",
    "replicated_post_plot = sns.histplot(data = replicated_post, x=\"pi\")\n",
    "\n",
    "#plt.xticks(np.arange(0.2,0.8,0.3))\n",
    "\n",
    "replicated_post_plot.set(xticks=[0.2,0.5,0.8])\n",
    "sns.despine()"
   ]
  }
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